24 ßčéìĊęǰ1 đøČęĂÜ ÖãđÖèæŤđïČĚĂÜêšîđÖĊę÷üÖĆïÖćøîĆï ßčéÖĉÝÖøøöÖćøđøĊ÷îøĎšüĉßćÙèĉêýćÿêøŤǰ ǰǰǰêĆüĂ÷ŠćÜìĊęǰ3 êšĂÜÖćøÿøšćÜÝĞćîüîÙĎŠïüÖÿĊęĀúĆÖÝćÖêĆüđú×ǰǰ ǰ ǰ ǰ ǰǰǰēé÷ĒêŠúąĀúĆÖ ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰĔßšêĆüđú×ĕöŠàĚĞćÖĆî ÝąÿøšćÜĕéšÖĊęÝĞćîüî ĀúĆÖĀîŠü÷Ĕßšđú×ēééǰǰ , ,ǰǰ ǰǰǰǰĒ÷ÖđðŨîǰǰǰÖøèĊǰ ǰǰǰǰǰÖøèĊìĊęǰǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰǰǰ ǰǰǰǰǰǰǰǰǰǰöĊǰǰǰǰǰǰüĉíĊǰǰǰǰ ĀúĆÖóĆîǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ3, 4, 6ǰĀøČĂǰ öĊǰǰǰǰǰǰüĉíĊǰǰǰÿööêĉĔßšǰǰ ĀúĆÖøšĂ÷ǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ4, 6ǰĀøČĂǰ öĊǰǰǰǰǰǰüĉíĊǰǰǰÿööêĉĔßšǰǰ ĀúĆÖÿĉïǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ6ǰĀøČĂǰ öĊǰǰǰǰǰǰüĉíĊǰǰǰ ĀúĆÖóĆî ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰÙČĂǰǰǰ ǰǰǰǰǰǰǰǰ= ǰÝĞćîüîǰǰ ǰǰǰǰǰǰǰÖøèĊìĊęǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰ ǰǰǰĀøČĂǰǰ ǰǰǰǰǰǰǰǰöĊǰǰǰǰǰǰüĉíĊǰǰǰÿööêĉĔßšǰǰǰǰǰǰǰǰǰ ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰĀúĆÖóĆîǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰ ǰ3, 6ǰĀøČĂǰǰ ĔßšǰǰĕöŠĕéš öĊǰǰǰǰǰüĉíĊǰǰǰǰÿööêĉĔßšǰǰǰǰǰ ĀúĆÖøšĂ÷ǰǰđĀúČĂđú×ēééǰǰ 6ǰĀøČĂǰ ǰǰǰǰǰǰǰǰǰöĊǰǰǰǰǰǰüĉíĊǰǰǰÿööêĉĔßšǰǰǰǰǰǰ ĀúĆÖÿĉïǰǰǰđĀúČĂđú×ēééǰǰ6ǰĀøČĂǰ ǰǰǰǰǰǰǰǰǰöĊǰǰǰǰǰǰüĉíĊǰǰ ĀúĆÖóĆî ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰĀøČĂǰǰÙČĂǰǰ ǰǰǰǰǰǰǰ= ǰÝĞćîüîǰǰ ÖøèĊìĊęǰǰǰǰ ǰǰǰǰÖøèĊìĊęǰǰǰǰ = + = ǰǰǰǰÝĞćîüî ←42 нр COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
25 ßčéìĊęǰ1 đøČęĂÜ ÖãđÖèæŤđïČĚĂÜêšîđÖĊę÷üÖĆïÖćøîĆï ßčéÖĉÝÖøøöÖćøđøĊ÷îøĎšüĉßćÙèĉêýćÿêøŤǰ ÖãÖćøïüÖǰǰëšćÖćøìĞćÜćîĀîċęÜöĊüĉíĊÖćøìĞćǰ k üĉíĊǰÙČĂǰüĉíĊìĊęǰ1 ëċÜüĉíĊìĊęǰǰk ēé÷ìĊęǰÖćøìĞćÜćîüĉíĊìĊęǰ1 öĊüĉíĊìĞćǰn1 üĉíĊǰÖćøìĞćÜćîüĉíĊìĊęǰ2 öĊüĉíĊìĞćǰn2 üĉíĊǰ ÖćøìĞćÜćîüĉíĊìĊęǰ3 öĊüĉíĊìĞćǰn3 üĉíĊǰļÖćøìĞćÜćîüĉíĊìĊęǰk öĊüĉíĊìĞćǰnk üĉíĊǰĒúąüĉíĊÖćø ìĞćÜćîĒêŠúąüĉíĊĒêÖêŠćÜÖĆîĒúšüÝĞćîüîüĉíĊÖćøìĞćÜćîîĊĚđìŠćÖĆïǰn1 + n2 + n3 ǰļǰ ǰOk üĉíĊ 1) êšĂÜÖćøÿøšćÜÝĞćîüîÙĎŠïüÖÿĊęĀúĆÖÝćÖêĆüđú×ǰǰ ǰ ǰ ǰ ǰǰǰēé÷ĒêŠúąĀúĆÖ ĔßšêĆüđú×ĕöŠàĚĞćÖĆî ÝąÿøšćÜĕéšÖĊęÝĞćîüîǰǰ(5 ÙąĒîî) ĀúĆÖĀîŠü÷Ĕßšđú×ēééǰǰ , ,ǰǰ ǰǰǰǰĒ÷ÖđðŨîǰǰǰÖøèĊǰ ǰǰǰǰǰÖøèĊìĊęǰǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰǰǰ ǰǰǰǰǰǰǰǰǰǰöĊļļļüĉíĊǰ ĀúĆÖóĆîǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ3, 4, 6ǰĀøČĂǰ öĊļļļüĉíĊǰǰǰÿööêĉĔßšǰǰ ĀúĆÖøšĂ÷ǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ4, 6ǰĀøČĂǰ öĊļļļüĉíĊǰǰǰÿööêĉĔßšǰǰ ĀúĆÖÿĉïǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰǰ6ǰĀøČĂǰ öĊļļļüĉíĊǰǰǰ ĀúĆÖóĆî ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ļļļļļ ļļļļļ ļļļļļ ļļļļļ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰ ǰÙČĂffǰļļļļļļļÝĞćîüîǰ ÖøèĊìĊęǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰ ǰǰǰĀøČĂǰǰ ǰǰǰǰǰǰǰǰöĊļļļüĉíĊǰǰǰÿööêĉĔßšǰǰǰǰǰ ǰĀúĆÖóĆîǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰ ǰ3, 6ǰĀøČĂǰǰ ĔßšǰǰĕöŠĕéš öĊļļļüĉíĊǰǰǰǰÿööêĉĔßšǰǰǰǰǰ ĀúĆÖøšĂ÷ǰǰđĀúČĂđú×ēééǰǰ 6ǰĀøČĂǰ ǰǰǰǰǰǰǰǰǰöĊļļļüĉíĊǰǰǰÿööêĉĔßšǰǰǰǰǰǰ ĀúĆÖÿĉïǰǰǰđĀúČĂđú×ēééǰǰ6ǰĀøČĂǰ ǰǰǰǰǰǰǰǰǰöĊļļļüĉíĊǰǰ ĀúĆÖóĆî ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ļļļļļ ļļļļļ ļļļļļ ļļļļļ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰĀøČĂǰǰ ǰÙČĂffǰļļļļļļļÝĞćîüîǰ ǰǰǰǰÖøèĊìĊęǰǰǰǰ ǰǰǰǰÖøèĊìĊęǰǰǰǰ = = ǰÝĞćîüî ïĆêøÖĉÝÖøøöìĊęǰ 1.3 ĀúĆÖÖćøïüÖ×ĂÜÖãđÖèæŤđïČĚĂÜêšîđÖĊę÷üÖĆïÖćøîĆï Br 43 нс COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
26 ßčéìĊęǰ1 đøČęĂÜ ÖãđÖèæŤđïČĚĂÜêšîđÖĊę÷üÖĆïÖćøîĆï ßčéÖĉÝÖøøöÖćøđøĊ÷îøĎšüĉßćÙèĉêýćÿêøŤǰ 2) öĊđú×ēééĂ÷ĎŠǰ5 êĆüǰÙČĂǰ0, 3, 4, 6, 7 ëšćêšĂÜÖćøÿøšćÜÝĞćîüîÙĎŠïüÖÿćöĀúĆÖ àċęÜðøąÖĂïéšü÷êĆüđú×ēééđĀúŠćîĊĚǰǰēé÷ĒêŠúąĀúĆÖĔßšđú×ĕöŠàĚĞćÖĆîǰÝąÿøšćÜĕéšÖĊęÝĞćîüî (5 ÙąĒîî) ĀúĆÖĀîŠü÷Ĕßšđú×ēééǰǰ, ,ǰǰǰǰĒ÷ÖđðŨîǰǰǰÖøèĊǰ ÖøèĊìĊęǰǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰǰ ǰǰǰǰǰǰǰǰǰǰǰöĊ.........ǰüĉíĊǰ ĀúĆÖøšĂ÷ǰǰđĀúČĂđú×ēééǰǰǰêĆüǰÙČĂǰ3, 4, 6 ĀøČĂǰǰ7 ǰöĊ.........ǰüĉíĊǰǰǰÿööêĉĔßšǰǰ ĀúĆÖÿĉïǰǰǰǰđĀúČĂđú×ēééǰǰêĆüǰÙČĂǰ4, 6 ĀøČĂǰ7 ǰöĊ.........ǰüĉíĊǰ ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰ ÙČĂǰǰǰ..................= ......... ǰÝĞćîüîǰ ÖøèĊìĊęǰǰǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰǰĀøČĂǰ ĀúĆÖĀîŠü÷đðŨîǰǰǰǰǰĀøČĂǰǰǰǰǰǰǰǰǰ ǰöĊ.........ǰüĉíĊǰǰÿööêĉĔßšǰǰǰǰǰ ĀúĆÖøšĂ÷ǰǰđĀúČĂđú×ēééǰ ǰ3, 6ǰĀøČĂǰ7ǰǰǰöĊ.........ǰüĉíĊǰǰÿööêĉĔßšǰǰǰǰ ĔßšǰǰĕöŠĕéš ĀúĆÖÿĉïǰǰǰǰđĀúČĂđú×ēééǰǰ, 6 ĀøČĂ 7ǰǰǰǰǰöĊ.........ǰüĉíĊǰ ĀúĆÖøšĂ÷ ĀúĆÖÿĉï ĀúĆÖĀîŠü÷ ÝĞćîüîüĉíĊ ?ÝĞćîüîüĉíĊìĊęÿøšćÜÝĞćîüîÙĎŠǰǰǰĀúĆÖǰǰĀúĆÖĀîŠü÷đðŨîǰǰǰĀøČĂǰǰ ÙČĂǰǰǰ..................= ......... ǰÝĞćîüîǰ ?ÝĞćîüîÙĎŠïüÖÿćöĀúĆÖēé÷ĒêŠúąĀúĆÖĔßšđú×ĕöŠàĚĞćÖĆîǰÝąÿøšćÜĕéšǰ ÖøèĊìĊęǰǰǰǰ ǰÖøèĊìĊęǰǰǰǰ = ......... = ......... ÝĞćîüîǰ oa44 нт COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ Part 2ǰĒôÙìĂđøĊ÷ú factorial COMBINATORIC and PROBABILITY øć÷üĉßćÙĂöïĉîćìĂøĉÖĒúąÙüćöîŠćÝąđðŨî ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰøć÷üĉßćđóĉęöđêĉöÖúčŠöǰ1øĀĆÿüĉßćǰÙ30203 îć÷ïčâđÿøĉåǰǰÝĆîìøŤìĉîǰ ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ǰǰǰǰ ēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ǰîÙøýøĊíøøöøćßÿĞćîĆÖÜćî đ×êóČĚîìĊęöĆí÷öýċÖþćđ×êǰ12ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ • 47 ой COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 13 48 ใน oereootttarerernererneostdteteoo onstnostootssesmntsetttttttinoottstemenesttttsrssrosessrsrrssrsssoessoe ок COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 14 öćýċÖþćÖćøđ×Ċ÷îÿĆâúĆÖþèŤĒìîÖćøÙĎèÖĆî ×ĂÜÝĞćîüîđêĘöïüÖǰǰìĊęđøĊ÷ÖüŠćǰǰ ĒôÖìĂđøĊ÷úǰǰÝćÖǰǰêĂîìĊęǰǰǰǰĒôÖìĂđøĊ÷úǰǰ ÖĆîĕéšĒúšüÙŠą ลอง 49 ssasneoooopoaoapgggsg srs-ts-oETTTTODTTTSOTTTTSTSO-erttttTTATSstostttttttttsTTTTessrsttt-TDTTettt.pro о2 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 15 êĂîìĊęǰǰ ĒôÖìĂđøĊ÷ú ไร50 eeeeeennoooeeeneeooeoooa sosttrseossnittttnssrseeonssnsstotsnsrotttttstrsetrettsrsserntsore ом COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 16 ïìîĉ÷ćöǰǰ ëšć nǰǰđðŨîÝĞćîüîđêĘöïüÖǰǰĒôÖìĂđøĊ÷úǰǰnǰǰ( factorial )ǰǰ ÙČĂǰǰñúÙĎè×ĂÜÝĞćîüîđêĘöïüÖ êĆĚÜĒêŠǰǰ1 ëċÜǰǰnǰǰĒúąǰǰđ×Ċ÷îĒìîéšü÷ǰǰnǰ êĆüĂ÷ŠćÜǰǰ 1! = 1 2! = 2 × 1 3! = 3 × 2 × 1 4! = 4 × 3 × 2 × 1 5! = 5 × 4 × 3 × 2 × 1 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 n! = n × (n - 1) × (n - 2) × × 3 × 2 × 1 (n - 1)! = (n - 1) × (n - 2) × (n - 3) × × 3 × 2 × 1 (n - 2)! = (n - 2) × (n - 3) × (n - 4) × × 3 × 2 × 1 (n + 1)! = (n + 1) × n × (n - 1) × × 3 × 2 × 1 (n + 2)! = (n + 2) × (n + 1) × n × × 3 × 2 × 1 (2n + 1)! = (2n + 1) × 2n × (2n - 1) × × 3 × 2 × 1 ĒúąǰǰÖćøđ×Ċ÷îǰǰǰǰ n! = n × (n - 1) × (n - 2) × × 3 × 2 × 1 öĊÙüćöĀöć÷đéĊ÷üÖĆï n! = 1 × 2 × 3 × × (n - 2) × (n - 1) × n êĂîìĊęǰǰ ĒôÖìĂđøĊ÷ú ไร51 snssosssooooooesssoesttrsssg ottttreteestttttntetntsttosnnnsttfttatsnssrsstssttsoftnsssnesrssre он COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 17 Öćøđ×Ċ÷îÝĞćîüîĔîøĎðĒôÖìĂđøĊ÷úǰǰđóČęĂĒÿéÜÖćøÙĎèÖĆî×ĂÜÝĞćîüîđêĘöïüÖǰǰÿćöćøëđ×Ċ÷î ĕéšĀúć÷øĎðĒïïĔîÖćøĒÿéÜÙüćöĀöć÷×ĂÜǰǰn! ǰǰđߊî đîČęĂÜÝćÖ 5! = 5 × 4 × 3 × 2 × 1 Ēúąǰǰ 2! = 2 × 1 éĆÜîĆĚî 5! = 5 × 4 × 3 × 2! ĀøČĂ 5! = 5 × 4 × 3! đóøćąǰǰ 3! = 3 × 2 × 1 ĀøČĂ 5! = 5 × 4! đóøćąǰǰ 4! = 4 × 3 × 2 × 1 îĆęîÙČĂǰǰÿćöćøëđ×Ċ÷î n! ĔĀšĂ÷ĎŠĔîøĎð×ĂÜĒôÖìĂđøĊ÷ú×ĂÜÝĞćîüîđêĘöïüÖĔéǰėǰ ìĊęöĊÙŠćîšĂ÷ÖüŠćǰǰn ĕéšéĆÜîĊĚ ÝćÖ n! ǰǰ= n × (n - 1) × (n - 2) × (n - 3) × × 3 × 2 × 1 ĀøČĂ = n × (n - 1) × (n - 2) × (n - 3)! ĀøČĂ = n × (n - 1) × (n - 2)! ĀøČĂ = n × (n - 1)! đîČęĂÜÝćÖÖćøđ×Ċ÷îÝĞćîüîĔîøĎðĒôÖìĂđøĊ÷úǰǰÿćöćøëđ×Ċ÷îĕéšđÞóćąÙüćöÿĆöóĆîíŤ×ĂÜÝĞćîüîđêĘöïüÖ đìŠćîĆĚîǰ ǰ éĆÜîĆĚîǰ ǰ ÝĞćîüîđêĘöïüÖĔéǰ ėǰ ǰ Ýąÿćöćøëđ×Ċ÷îĒÿéÜĕéšéšü÷ÖćøÙĎèÖĆî×ĂÜÝĞćîüîđêĘöïüÖǰ ĕéšĀúć÷øĎðĒïïǰǰđߊîǰǰÝąđ×Ċ÷îĒÿéÜÙüćöÿĆöóĆîíŤ×ĂÜǰǰ10ǰǰĔîøĎðĒôÖìĂđøĊ÷úĕéšđðŨî 10 = 120 5 × 4 × 3 × 2 × 1 5! 5! = = = 12 6 × 2 3 × 2 × 2 3!2! ĀøČĂ 10 = 10 × 9! 9! ǰǰÖĘĕéš ĀøČĂÝąÿćöćøëđ×Ċ÷îǰǰǰǰĔîøĎðĒôÖìĂđøĊ÷úĕéšđðŨî 120 = 5! ĀøČĂǰǰǰǰ120 = 6! 3! ǰĕéšđߊîÖĆî ǰîĆÖđøĊ÷îúĂÜĀćÙüćöÿĆöóĆîíŤ ǰǰ×ĂÜÝĞćîüîĂČęîǰėǰǰîąÙą +52 rts.rs-rnsorsrerSTTTTTDtsstsmssrsss.BR rOออนนางอวาอาาอวงานสรารานมคาอ0ากอนรกาอนาอางอองรsAาารตนอด оо COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 18 ĒôÖìĂđøĊ÷úýĎî÷Ť ÝćÖïìîĉ÷ćö×ĂÜĒôÖìĂđøĊ÷úǰǰn ÖĞćĀîéĔĀšǰǰn đðŨîÝĞćîüîđêĘöïüÖǰǰÝąÿćöćøëĒÿéÜ ÙüćöÿĆöóĆîíŤđóČęĂĀćǰǰ0! ĕéšǰǰēé÷ÖćøÖĞćĀîéǰǰn đðŨîÝĞćîüîđêĘöïüÖĔéǰėǰǰĕéšéĆÜîĊĚ ÝćÖïìîĉ÷ćöǰǰnǰǰđðŨîÝĞćîüîđêĘöïüÖǰǰĒúąǰǰǰǰđðŨîÝĞćîüîđêĘöïüÖ ÖĞćĀîéĔĀšǰǰn = 1 óĉÿĎÝîŤ đîČęĂÜÝćÖ n! = n × (n - 1) × (n - 2) × (n - 3) ×...× 3 × 2 × 1 = n × (n - 1)! ëšć n = 1ǰǰǰ Ýąĕéš 1! = 1 × (1 - 1)! = 1 × (0)! = 0! (1ǰǰđðŨîđĂÖúĆÖþèŤÖćøÙĎè) éĆÜîĆĚî 1! = 0! ĒúąđîČęĂÜÝćÖ 1! = 1 éĆÜîĆĚî 0! = 1 0 = ? đøćúĂÜÖĞćĀîéǰǰn đðŨîÝĞćîüîđêĘöïüÖĂČęîǰė đߊîǰǰ2 ĀøČĂ 3 ÖćøóĉÿĎÝîŤǰǰ 0! ÝąđìŠćÖĆïǰǰ0 ĀøČĂĕöŠǰǰ úĂÜĕðìĞćÖĉÝÖøøöǰǰ0! ÖĆîîąÙą สองสาม 53 rtsrsennsrresresrsrstseetttttttttssttsetnsstssnssreserssttg mnoeortrnnsrosornrssoneonsemsneooaorssssrossssrsssssotnsoeorssssrssrsssonoe о6 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 19 ÝčéðøąÿÜÙŤÖćøđøĊ÷îøĎšǰǰîĞćÙüćöøĎšđøČęĂÜĒôÖìĂđøĊ÷úǰǰn ĕðĔßšĔîÖćøĒÖšðŦâĀćĕéš ÙĞćÿĆęÜǰǰ ÝÜĒÿéÜÖćøóĉÿĎÝîŤüŠćǰǰ0! = 1ǰǰđöČęĂÖĞćĀîéĔĀšǰǰn = 2ǰǰĒúąǰǰn = 3 üĉíĊìĞć ÖĉÝÖøøö 0! 0! = 1 ัอมออ540นง กลrnsrsnนrsอนมานนnsrosTนาานานอางTอนนงคsรsrssssมssssงอsรnop osoaasassss ор COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 20 ÝÜđ×Ċ÷îÝĞćîüîêŠĂĕðîĊĚĔîøĎðÖćøÖøąÝć÷×ĂÜñúÙĎè×ĂÜÝĞćîüîđêĘöïüÖ êŠĂĕðĂĊÖǰ 5 óÝîŤ 1. 8! 2. 20! 3. (n + 5)! 4. (n - 5)! 5. (2n + 4)! 6. (2n - 1)! üĉíĊìĞć 1. 8! = 8 × 7 × 6 × 5 × 4! 2. 20! = 20 × 19 × 18 × 17 × 16! 3. (n + 5)! = (n + 5)(n + 4)(n + 3)(n + 2)(n + 1)! 4. (n - 5)! = (n - 5)(n - 6)(n - 7)(n - 8)(n - 9)! 5. (2n + 4)! = (2n + 4)(2n + 3)(2n + 2)(2n + 1)(2n)! 6. (2n - 1)! = (2n - 1)(2n - 2)(2n - 3)(2n - 4)(2n - 5)! êĆüĂ÷ŠćÜìĊęǰǰ2.1 đøćöćđøĊ÷îøĎšÖćøđ×Ċ÷îÝĞćîüîĔîøĎðĒôÖìĂđøĊ÷ú ÝćÖêĆüĂ÷ŠćÜêŠĂĕðîĊĚĕéšđú÷îąÙą ←55 ornpnpeeosorsrssnsoprsssnssnssssnnsnosesssorse nooeaoesoersarsrnooerosetsseseoorsannsrrosottrnsttsoesoossrsnssrssetsetssrstte ос COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 21 ÝÜĀćÙŠć×ĂÜÝĞćîüîêŠĂĕðîĊĚ 1. 6! 2. 7!0! 5!3! ǰ 10! 3!7! 4. 12! (12 - 3)!3! 5. 9! (9 - 9)!0! 6. 20! (20 - 4)!4! üĉíĊìĞć 1. 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 2. 7!0! 5!3! = 7 × 6 × 5! × 1 5! × 3 × 2 × 1 = 7 × 6 3 × 2 = 7 10! 3!7! = 10 × 9 × 8 × 7! 3!7! = 10 × 9 × 8 3 × 2 = 720 6 = 120 êĆüĂ÷ŠćÜìĊęǰǰ2.2 56 องคมนต5 Trtrsprsssrorrsrosoortsrssrsrsrssgsoosg Boooanseeosnoasssssoases от COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 22 12! (12 - 3)!3! = 12! 9!3! = 12 × 11 × 10 3 × 2 = 1,320 6 = 220 ǰǰ 9! (9 - 9)!0! = 9! 0!0! = 9! 1×1 = 9! ǰǰ 20! (20 - 4)!4! = 20! 16!4! = 20 × 19 × 18 × 17 × 16! 16! × 4 × 3 × 2 × 1 = 20 × 19 × 18 × 17 4 × 3 × 2 × 1 = 4,845 *57 rrsozosozssszn onsoeesoaaosasnesnsnoosstess 6й COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 23 ÝÜđ×Ċ÷îÝĞćîüîêŠĂĕðîĊĚĔîøĎðĒôÖìĂđøĊ÷úǰǰ 15 × 14 × 13 × 12 ǰǰ 2 n - 5n + 6ǰǰ (2n + 2)(2n + 1)(2n) 4. n(n - 1)(n - 2)(n - 3) üĉíĊìĞć 15 × 14 × 13 × 12 = 15 × 14 × 13 × 12 × 11! 11! = 15! 11! 2 n - 5n + 6 = (n - 2)(n - 3) = (n - 2)(n - 3)(n - 4)! (n - 4)! = (n - 2)! (n - 4)! (2n + 2)(2n + 1)(2n) = (2n + 2)(2n + 1)(2n)(2n - 1)! (2n - 1)! = (2n + 2)! (2n - 1)! 4. n(n - 1)(n - 2)(n - 3) = n(n - 1)(n - 2)(n - 3)(n - 4)! (n - 4)! = n! (n - 4)! êĆüĂ÷ŠćÜìĊęǰǰ2.3 58 นางออง oestssrsrnsorsoosrsssrssstststtssttstserssssrosspgesssssssg zesosottttttrrssreostttttlrssrrtsesttetnonrtesssrssnreseossstttiosstssnsssssnssensnnsostsstsssstsonn nsrs 6к COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 24 ÝÜđ×Ċ÷îÝĞćîüîêŠĂĕðîĊĚĔîøĎðìĊęĕöŠöĊĒôÖìĂđøĊ÷ú 1. (n - 1)!(n + 2)! n!(n - 2)! 2. n!(n + 2)! (n - 1)!(n + 1)! 3. (n - 2)! (n + 1)! 4. (n+1)!(n + 2)! (n + 3)! üĉíĊìĞć ǰǰ (n - 1)!(n + 2)! n!(n - 2)! = (n - 1)(n - 2)!(n + 2)(n + 1)n! n!(n - 2)! ļļ= (n - 1)(n + 2)(n + 1) ǰ n!(n + 2)! (n - 1)!(n + 1)! = n(n - 1)!(n + 2)(n + 1)! (n - 1)!(n + 1)! = n(n + 2) ǰǰ (n - 2)! (n + 1)! = (n - 2)! (n + 1)(n)(n - 1)(n - 2)! = 1 (n + 1)(n)(n - 1) = 2 1 n(n - 1) ǰǰ (n+1)!(n + 2)! (n + 3)! = (n+1)!(n + 2)! (n + 3)(n + 2)! = n + 1 n + 3 êĆüĂ÷ŠćÜìĊęǰǰ2. *59 ntrnsrsersororsroorsressts oosoaasoe 62 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 29 4.1 7! 11! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 4.2 10! 5!3!2! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 4.3 n! (n - 3)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 4.4 (n + 1)! (n - 1)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 4.5 (n - 1)!(n + 2)! n!(n - 2)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ☆64 enesasesosegsessnsnsnspog ooaeaoooaoaoeooos 6м COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 30 îĂÖÝćÖÖćøđ×Ċ÷îÿĆâúĆÖþèŤĒìîÖćøÙĎèÖĆî×ĂÜÝĞćîüîđêĘöïüÖ ĔîøĎðĒôÖìĂđøĊ÷úĒúšüǰǰđøćÿćöćøëÿøšćÜÿöÖćøĔîøĎðĒôÖìĂđøĊ÷úǰǰ ĒúąĒÖšÿöÖćøĕéš ĕéšđüúćđøĊ÷îøĎšüĉíĊÖćøĒÖšÿöÖćøĔîøĎðĒôÖìĂđøĊ÷úǰǰ ÝćÖêĂîìĊęǰǰǰǰÿöÖćøĒôÖìĂđøĊ÷úǰǰ ÖĆîĕéšĒúšüÙŠą 665ไล nrrrsrsssronoooorssrsssorsorsrssssensnpsssosna neeoonsoorrnoaesesnsrsotosrsttasossss 6н COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 31 êĂîìĊęǰǰ ÿöÖćøĒôÖìĂđøĊ÷ú อาจ66 oreereeeereesesoosessrnsorssessrrsnsrseosmssnossass noeoornnssttssrooesmossosssoooeerrressrssetensnss 6о COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 32 đöČęĂĀćÙŠćĒôÖìĂđøĊ÷úǰĒúąđ×Ċ÷îÝĞćîüîĔîøĎðĒôÖìĂđøĊ÷úĔîøĎðÖćøÙĎèÖĆî×ĂÜÝĞćîüîđêĘöïüÖ ĕéšĒúšü đøćÿćöćøëîĞćÙüćöøĎšìĊęĕéšĕðĒÖšÿöÖćøǰǰìĊęĂ÷ĎŠĔîøĎðĒôÖìĂđøĊ÷úĕéšéĆÜêĆüĂ÷ŠćÜêŠĂĕðîĊĚ ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰǰ n ! (n - 3) ! = 720 üĉíĊìĞć n ! (n - 3) ! = 720 n(n - 1)(n - 2)(n - 3) ! (n - 3) ! = 720 n(n ı 1)(n ı 2) = 10 × 9 × 8 n(n ı 1)(n ı 2) = 10(10 ı 1)(10 ı 2) éĆÜîĆĚîǰ n = 10 ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰ n! (n - 2)! = 6 üĉíĊìĞć n! (n - 2)! = 6 n(n - 1)(n - 2)! (n - 2)! = 6 n(n - 1) = 3 × 2 éĆÜîĆĚîǰ n = 3 êĆüĂ÷ŠćÜìĊęǰǰ2.5 êĂîìĊęǰǰ ǰǰÿöÖćøĒôÖìĂđøĊ÷ú êĆüĂ÷ŠćÜìĊęǰ 2.6 Thtt 67 gpgsong.eegegngeo-spsesgrsapgnsgggogggong.ge nsteosootnttotneotorotntessrssrrtnsrssrsnrsnnttttosoettstnsstssrsrs 66 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 33 ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰǰ (n + 2)! n! = 30 üĉíĊìĞć (n + 2)! n! = 30 (n + 2)(n + 1)n! n! = 30 (n + 2)(n + 1) = 30 (n + 2)(n + 1) = 6 × 5 ĒÿéÜüŠćǰǰǰ n + 2 = 6 Ēúąǰǰn + 1 = 5 éĆÜîĆĚî n = 4 ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰǰ (n + 1) ! (n - 1) ! = 1,640 üĉíĊìĞć (n + 1) ! (n - 1) ! = 1,640 (n + 1)(n)(n - 1)! (n - 1)! = 1,640 (n + 1)n = 1,640 (n + 1)n = 41 × 40 n + 1 = 41 éĆÜîĆĚî n = 40 êĆüĂ÷ŠćÜìĊęǰ 2.7 êĆüĂ÷ŠćÜìĊęǰ 2.8 8 68 nnprggossnssnngessesggpnspgnsg neroeoconrerstrtrerosoeressnartoanretentteesitthessoerrosntotttsesstnsse 6р COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 34 ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰǰ (n - 1) ! (n - 3) ! = 20 üĉíĊìĞć (n - 1) ! (n - 3) ! = 20 (n - 1)(n - 2)(n - 3) ! (n - 3) ! = 20 (n ı 1)(n ı 2) = 5 × 4 Ýąĕéš n ı 1 = 5 ĀøČĂǰǰǰǰǰn ı 2 = 4 éĆÜîĆĚîǰ n = 6 ÝÜĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn ÝćÖÿöÖćøǰǰǰ 8!n! (n - 10)! = 10!n! (n - 8)! üĉíĊìĞć 8!n! (n - 10)! = 10!n! (n - 8)! (n - 8)! (n - 10)! = 10! 8! (n - 8)(n - 9)(n - 10)! (n - 10)! = 10 × 9 × 8! 8! (n - 8)(n - 9) = 10×9 Ýąĕéšǰǰn - 8 = 10ǰǰĀøČĂǰǰǰǰn - 9 = 9 éĆÜîĆĚîǰǰǰǰǰn = 18 êĆüĂ÷ŠćÜìĊęǰ 2.9 êĆüĂ÷ŠćÜìĊęǰ 2.10 9งสาทอง 69 nttrerrssrrrsorsersnrtttstsenrtrssossvsessrn ns.oonnottssseennoroaosnsrsorssnnssssssrrssrnssssstssttsnrsessns 6с COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 35 öćòřÖĒÖšÿöÖćøĔîøĎðĒôÖìĂđøĊ÷ú ÝćÖĒïïòřÖìĊęǰǰǰǰÖĆîĕéšđú÷îąÙą ĀćÖîĆÖđøĊ÷îöĊךĂÿÜÿĆ÷ǰǰĔĀšÿĂïëćöÙøĎñĎšÿĂî ĕéšìĆîìĊîąÙą 70 ออกมหาสมาคม arpneafngeopengeoggopgrsegengsosrspeeg_s.rsp.rggnggnggng.sn toreomoteoroetnssssoemottttsrsorssssvsssesststtsssnttttts 6т COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 36 ÝčéðøąÿÜÙŤÖćøđøĊ÷îøĎš : îĞćÙüćöøĎšđøČęĂÜĒôÖìĂđøĊ÷úǰǰn ĕðĔßšĔîÖćøĒÖšðŦâĀćĕéš ÙĞćÿĆęÜǰǰ óĉÝćøèćÿöÖćøĒôÖìĂđøĊ÷úêŠĂĕðîĊĚ ĒúšüĒÿéÜüĉíĊÖćøĀćÙŠćǰǰn êĆüĂ÷ŠćÜ ÝÜĀćÙŠćǰǰn ÝćÖÿöÖćø n! (n - 4)! = 840 üĉíĊìĞć n! (n - 4)! = 840 n(n - 1)(n - 2)(n - 3)(n - 4)! (n - 4)! = 7 × 6 × 5 × 4 n(n - 1)(n - 2)(n - 3) = 7 × 6 × 5 × 4 éĆÜîĆĚî n = 7 1. n! (n - 3)! = 60 üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 2. n! (n - 3)! = 63(n - 1)! (n - 2)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ĒïïòřÖìĊęǰǰ2. กลางดง 71 Ttterosrssrseessrnssrpgonessttrrsnssassssssssrssoss aooonnsoerssoornooeosoorsrrtttersernsroeseroserssssennsassn рй COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 37 3 (n + 2)! (n + 1)! = 800 üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ 4 n! (n - 2)! = (n + 1)! (n - 3)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ วาจา 72 rngeponsnsosspgngnesgsgsgggsspgggrsssnnsng rotooocoeresooontorostttilonrosrnettttssnetrsntttoeeossstnnoststeessorsssttttsstssae рк COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 38 . (n + 4)! 2 (n - 2)! ª º « » ¬ ¼ = (n + 5)! (n - 1)! üĉíĊìĞć ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļļ ออด73 ttheresrnsrnstrttttstoootttetssttntttesasonssonsra oeroteeestsoeeeooarromnoneotttnttnesnnstsosstsstttssnn р2 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøć÷üĉßćÙèĉêýćÿêøŤđóĉęöđêĉöǰǰǰǰđøČęĂÜÙüćöîŠćÝąđðŨîǰǰßĆĚîöĆí÷öýċÖþćðŘìĊęǰǰ6 đúŠöìĊęǰǰǰǰĒôÖìĂđøĊ÷ú 39 ÿøčðïìđøĊ÷î ïìîĉ÷ćöǰǰǰǰëšć nǰǰđðŨîÝĞćîüîđêĘöïüÖǰǰĒôÖìĂđøĊ÷úǰǰnǰǰ(factorial)ǰǰÙČĂǰǰñúÙĎè×ĂÜÝĞćîüîđêĘöïüÖ ǰêĆĚÜĒêŠǰ 1 ëċÜǰǰnǰǰĒúąǰǰđ×Ċ÷îĒìîéšü÷ÿĆâúĆÖþèŤǰǰn! ÿøčðÖćøéĞćđîĉîÖćøĔîøĎðĒôÖìĂđøĊ÷ú 1. ÿćöćøëđ×Ċ÷î n! ĔĀšĂ÷ĎŠĔîøĎð×ĂÜĒôÖìĂđøĊ÷ú×ĂÜÝĞćîüîĔéǰėǰǰìĊęöĊÙŠćîšĂ÷ÖüŠć n ĕéš éĆÜîĊĚ ÝćÖ n! = n × (n - 1) × (n - 2) × (n - 3) × × 3 × 2 × 1 ĀøČĂ = n × (n - 1) × (n - 2) × (n - 3)! ĀøČĂ = n × (n - 1) × (n - 2)! ĀøČĂ = n × (n - 1)! 2. ÿćöćøëĂíĉïć÷ĕéšüŠćǰǰǰ! = 1 3. ÿćöćøëđ×Ċ÷îÿöÖćøĔîøĎðĒôÖìĂđøĊ÷úǰǰĒúąĒÖšÿöÖćøĕéšǰǰ BP74 srpprssrggpssosresnsogpgsea oosoooetlnttttntrsorttiotostttestosttonttsoeottttsttntstttsertortsotttttstsoststtsosss рм COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
Part 3ǰÖćøđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜđÿšî Linear Permutation COMBINATORIC and PROBABILITY øć÷üĉßćÙĂöïĉîćìĂøĉÖĒúąÙüćöîŠćÝąđðŨî øć÷üĉßćđóĉęöđêĉöÖúčŠöǰ1øĀĆÿüĉßćǰÙ30203 îć÷ïčâđÿøĉåǰǰÝĆîìøŤìĉîǰ ēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ǰîÙøýøĊíøøöøćßÿĞćîĆÖÜćî đ×êóČĚîìĊęöĆí÷öýċÖþćđ×êǰ12 Be78 рн COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 1 ñúÖćøđøĊ÷îøĎš:: ĒÖšēÝì÷ŤðŦâĀćđÖĊę÷üÖĆïüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îĔîđßĉÜđÿšîêøÜĕéšǰĒúąĒÖšēÝì÷ŤðŦâĀć đÖĊę÷üÖĆïÖćøđøĊ÷ÜÿúĆïÖĆîĔîđßĉÜđÿšîêøÜĕéš ÖćøđøĊ÷ÜÿĆïđðúĊę÷î×ĂÜìĊęĒêÖêŠćÜÖĆîđßĉÜđÿšîêøÜǰǰđðŨîüĉíĊÖćøÝĆéđøĊ÷ÜÿĉęÜ×ĂÜĔîĒîüđÿšîêøÜĀøČĂđÿšî ēÙšÜǰēé÷ìĊęðúć÷ìĆĚÜÿĂÜךćÜ×ĂÜđÿšîĕöŠïøøÝïÖĆîǰǰēé÷üĉíĊđøĊ÷ÜÿĆïđðúĊę÷îĒïïđßĉÜđÿšî×ĂÜÿĉęÜ×ĂÜǰ n ÿĉęÜìĊęĒêÖêŠćÜÖĆîìĆĚÜĀöéÙøćüúą n ÿĉęÜǰĀøČĂÙøćüúąǰr ǰÿĉęÜǰđöČęĂǰr n d ǰ ēé÷ìĊęĒêŠúąêĞćĒĀîŠÜĔßš×ĂÜĕöŠ àĚĞćÖĆîǰǰàċęÜÖćøĀćÝĞćîüîüĉíĊÖćøÿĆïđðúĊę÷îđðŨîéĆÜîĊĚ ǰĀöć÷đĀêčǰǰǰ (1) đøćĂćÝÝąĀćÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îÝćÖÖãÖćøîĆïĕéšĂĊÖüĉíĊĀîċęÜ (2) đìÙîĉÙÖćøÝĆéđøĊ÷ÜĔĀšÿĉęÜ×ĂÜïćÜÿĉęÜĂ÷ĎŠĔĀšêĉéÖĆîđÿöĂǰĔĀšöĂÜøüöÿĉęÜìĊęêšĂÜÖćøĔĀšĂ÷ĎŠêĉéÖĆî đðŨîÿĉęÜ×ĂÜĀîċęÜÿĉęÜǰđöČęĂđøĊ÷ÜÿĆïđðúĊę÷îìĆĚÜĀöéĒúšüĔĀšÙĎèüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îĔîÖúčŠöéšü÷ǰ(öĆéöĂÜđðŨî ĀîċęÜ) (3) đìÙîĉÙÖćøÝĆéđøĊ÷ÜìĊęĔĀšÿĉęÜ×ĂÜïćÜÿĉęÜĕöŠĔĀšĂ÷ĎŠêĉéÖĆîđú÷ǰĔĀšÝĆéđøĊ÷ÜÿĉęÜ×ĂÜĂČęîÖŠĂîĒúšüîĞć ÿĉęÜ×ĂÜìĊęđĀúČĂìĊęĕöŠêšĂÜÖćøĔĀšêĉéÖĆîĕðĒìøÖøąĀüŠćÜÿĉęÜìĊęÝĆéĕüšĒúšüǰ(ÝĆéĂ÷ŠćÜĂČęîĒúšüĒìøÖ) êĆüĂ÷ŠćÜìĊęǰǰǰÝÜĀćÝĞćîüîüĉíĊìĊęÝąÝĆéêĆüĂĆÖþøÙĞćüŠćǰĶ46/%":ķǰĔĀšđðŨîÙĞćĔĀöŠǰēé÷ĕöŠÙĞćîċÜëċÜ ÙüćöĀöć÷ üĉíĊìĞć ÙĞćüŠćǰĶ46/%":ķǰðøąÖĂïéšü÷êĆüĂĆÖþøǰ6 êĆüǰêŠćÜÖĆî éĆÜîĆĚîǰÖćøÝĆéúĞćéĆïÿĉęÜ×ĂÜǰn ÿĉęÜǰìĊęĒêÖêŠćÜÖĆîÝąÝĆéĕéšǰ n!ǰüĉíĊ êĂï ? Ķ46/%":ķǰîĞćöćÝĆéđðŨîÙĞćĔĀöŠÝąÝĆéĕéšǰ 6!ǰǰǰ ǰǰǰ720 üĉíĊ ÖćøđøĊ÷ÜÿĆïđðúĊę÷î×ĂÜìĊęĒêÖêŠćÜÖĆîđßĉÜđÿšîêøÜǰǰ ǰǰǰǰǰǰ ÝĞćîüîǰ2 Ùćï ÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îĒïïđßĉÜđÿšî×ĂÜÿĉęÜ×ĂÜìĊęĒêÖêŠćÜÖĆîìĆĚÜĀöé n ÿĉęÜ ÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđìŠćÖĆï n! üĉíĊ ëšćöĊÿĉęÜ×ĂÜìĊęĒêÖêŠćÜÖĆîǰ n ÿĉęÜ êšĂÜÖćøîĞćöćÝĆéđøĊ÷ÜĒïïđßĉÜđÿšîǰÝĞćîüîǰǰr ÿĉęÜǰǰ r n d ǰǰǰǰǰǰÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđìŠćÖĆïǰ , ! ! n r nr n r n PP P n r üĉíĊ <๊79 • tttetrttnotareetererttotsteostttttrsorerrt ро COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 2 êĆüĂ÷ŠćÜìĊęǰǰǰöĊêĞćĒĀîŠÜÜćîüŠćÜĂ÷ĎŠǰ5 êĞćĒĀîŠÜǰàċęÜđðŨîêĞćĒĀîŠÜÿĞćĀøĆïßć÷ǰ3 êĞćĒĀîŠÜǰĒúąĀâĉÜǰ2 êĞćĒĀîŠÜǰǰëšćöĊñĎšÿöĆÙøđðŨîßć÷ǰ7 ÙîǰĀâĉÜǰ4 ÙîǰÝąöĊüĉíĊÝĆéÙîđךćìĞćÜćîĕéšÖĊęüĉíĊ üĉíĊìĞć öĊßć÷ÿöĆÙøǰ7 ÙîǰĒêŠêšĂÜÖćøđóĊ÷Üǰ3 ÙîǰÝąđúČĂÖĕéšǰ P7,3 ǰüĉíĊ ǰǰǰ 7! 7 3! ǰǰǰ ǰǰǰ 7! 4! ǰǰǰ ǰǰǰ 765 u u ǰǰǰ ǰǰǰ210ǰǰǰüĉíĊ öĊĀâĉÜÿöĆÙøǰ4 ÙîǰĒêŠêšĂÜÖćøđóĊ÷Üǰ2 ÙîǰÝąđúČĂÖĕéšǰ P4,2 ǰüĉíĊ ǰǰǰ 4! 4 2! ǰǰǰ ǰǰǰ 4! 2! ǰǰǰ ǰǰǰ 4 3u ǰǰǰ ǰǰǰ12ǰǰǰüĉíĊ êĂï ?ǰÝĞćîüîüĉíĊìĊęÝąÝĆéÙîđךćìĞćÜćîǰÙČĂǰ210 u 12 2,520 üĉíĊ êĆüĂ÷ŠćÜìĊęǰǰëšćêšĂÜÖćøÿúĆïêĆüĂĆÖþøÝćÖÙĞćüŠćǰAMPLITUDEǰ ēé÷ĕöŠÙĞćîċÜëċÜÙüćöĀöć÷ǰĕéšÖĊęÙĞćǰǰǰǰ ëšćÙĞćîĆĚîêšĂÜ×ċĚîêšîéšü÷ó÷ĆâßîąǰĒúąÿøąêšĂÜĕöŠêĉéÖĆî üĉíĊìĞć ĔîÙĞćüŠćǰAMPLITUDEǰöĊÝĞćîüîó÷ĆâßîąǰǰêĆüǰĒúąÿøąǰǰêĆü ×ĆĚîêĂîìĊęǰǰîĞćó÷ĆâßîąìĆĚÜǰǰêĆüđøĊ÷ÜÿĆïđðúĊę÷îÖĆîǰĕéšǰ 5! 120 ǰüĉíĊǰ ×ĆĚîêĂîìĊęǰǰîĞćÿøąìĆĚÜǰǰêĆüĒìøÖøąĀüŠćÜó÷Ćâßîąǰēé÷ĒìøÖĕéšǰǰêĞćĒĀîŠÜǰ ĀúĆÜÝćÖ ó÷ĆâßîąêĆüĒøÖǰĕéšǰ 5,4 P 5! 120ǰüĉíĊ M P L T D êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆï 120 120 14,400 u üĉíĊ êĆüĂ÷ŠćÜìĊęǰǰÙøĂïÙøĆüĀîċęÜðøąÖĂïéšü÷óŠĂǰĒöŠǰĒúąúĎÖǰ5ǰÙîǰëšćÙøĂïÙøĆüîĊĚêšĂÜÖćø×ĆïøëĕðđìĊę÷ü ìąđúēé÷Ĕßšøë÷îêŤìĊęöĊǰ7ǰìĊęîĆęÜǰēé÷ĔĀšóŠĂĀøČĂĒöŠđðŨîÙî×ĆïǰÝąöĊÝĞćîüîüĉíĊìĊęÝąÝĆéÿöćßĉÖĔîÙøĂïÙøĆü îĆęÜøë÷îêŤÙĆîîĊĚĕéšÖĊęüĉíĊ üĉíĊìĞć óŠĂǰĒöŠǰĒúąúĎÖǰ5ǰÙîǰøüöđðŨîǰ7ǰÙîǰöĊÙî×Ćïøëǰ2ǰÙîǰÙČĂǰóŠĂĒúąĒöŠ đúČĂÖóŠĂĀøČĂĒöŠöćîĆęÜĔîêĞćĒĀîŠÜÙî×Ćïĕéšǰ2ǰüĉíĊ đĀúČĂĂĊÖǰ6ǰÙîǰÝĆéîĆęÜĔîêĞćĒĀîŠÜìĊęđĀúČĂĕéšǰ 6!ǰüĉíĊ êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ2x720 = 1,440ǰüĉíĊ êĆüĂ÷ŠćÜìĊęǰǰÝÜĀćÝĞćîüîüĉíĊìĊęÝąÝĆéđéĘÖßć÷ǰ3ǰÙîǰĒúąđéĘÖĀâĉÜǰ4ǰÙîǰîĆęÜĔîĒëüēé÷ìĊęđéĘÖßć÷ÝąîĆęÜ ĔîêĞćĒĀîŠÜđú×ÙĎŠđÿöĂöĊìĆĚÜĀöéÖĊęüĉíĊ üĉíĊìĞć ÝĆéđéĘÖßć÷ǰ3ǰÙîǰîĆęÜĔîêĞćĒĀîŠÜìĊęǰ2 , 4 , 6ǰĕéšǰ3!ǰüĉíĊ ÝĆéđéĘÖĀâĉÜǰ4ǰÙîǰîĆęÜĔîêĞćĒĀîŠÜìĊęǰ1 , 3 , 5 , 7ǰǰĕéšǰ 4!ǰüĉíĊ êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ6x24 = 144ǰüĉíĊ อาคม80 ← nesrtsresrntrsrtttttotttrn attasrrsererrsrtsttttttrtnoestoetsre р6 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 3 êĆüĂ÷ŠćÜìĊęǰǰÝÜĀćñúøüö×ĂÜÝĞćîüîĀšćĀúĆÖìĊęÿøšćÜÝćÖđú×ēééǰǰ, 3 , 4 , 6 ēé÷êĆüđú×ĔîĒêŠúąĀúĆÖ ĕöŠàĚĞćÖĆî üĉíĊìĞć ÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îêĆüđú×ǰǰ, 3 , 4 , 6 đìŠćÖĆïǰ 4! 24 ǰüĉíĊ éĆÜîĆĚîöĊÝĞćîüîđêĘöïüÖĀšćĀúĆÖìĆĚÜĀöéǰ24 ÝĞćîüî Ĕîǰ24 ÝĞćîüîîĊĚöĊǰǰ, 3 , 4 , 6 ǰĒêŠúąêĆüðøćÖäĔîĒêŠúąĀúĆÖđìŠćÖĆïǰ 24 6 4 ǰÙøĆĚÜ ñúïüÖĔîĀúĆÖĀîŠü÷đìŠćÖĆïǰ 6 2346 u = 90 ñúïüÖĔîĀúĆÖÿĉïđìŠćÖĆïǰ90 x 10 = 900 ñúïüÖĔîĀúĆÖÿĉïđìŠćÖĆïǰ90 x 100 = 9000 ñúïüÖĔîĀúĆÖÿĉïđìŠćÖĆïǰ90 x 1000 = 90000 ñúïüÖĔîĀúĆÖÿĉïđìŠćÖĆïǰ90 x 10000 = 900000 êĂï éĆÜîĆĚîñúøüö×ĂÜÝĞćîüîđêĘöïüÖĀšćĀúĆÖìĆĚÜĀöéđìŠćÖĆïǰ999,990 êĆüĂ÷ŠćÜìĊęǰǰïøĉþĆìĒĀŠÜĀîċęÜöĊêĞćĒĀîŠÜÜćîüŠćÜĂ÷ĎŠǰ6ǰêĞćĒĀîŠÜêŠćÜÖĆîǰđðŨîêĞćĒĀîŠÜđÞóćąßć÷ǰ2 êĞćĒĀîŠÜǰêĞćĒĀîŠÜđÞóćąĀâĉÜǰ2ǰêĞćĒĀîŠÜǰĂĊÖǰ2ǰêĞćĒĀîŠÜđðŨîßć÷ĀøČĂĀâĉÜÖĘĕéšǰëšćöĊñĎšÿöĆÙøđðŨîßć÷ǰ 5ǰÙîǰĀâĉÜǰ4ǰÙîǰÝąöĊüĉíĊøĆïÙîđךćìĞćÜćîĕéšÖĊęüĉíĊǰǰ üĉíĊìĞć ßć÷ǰ5ǰÙîǰöĊêĞćĒĀîŠÜđÞóćąßć÷ǰ2ǰêĞćĒĀîŠÜǰÝĞćîüîüĉíĊìĊęÝąøĆïñĎšßć÷đךćìĞćÜćîđìŠćÖĆïǰ 5,2 5! 20 3! P ǰüĉíĊ ĀâĉÜǰ4ǰÙîǰöĊêĞćĒĀîŠÜđÞóćąĀâĉÜǰ2ǰêĞćĒĀîŠÜǰÝĞćîüîüĉíĊìĊęÝąøĆïñĎšĀâĉÜđךćìĞćÜćîđìŠćÖĆïǰ 4,2 4! 12 2! P üĉíĊ đĀúČĂßć÷ĒúąĀâĉÜǰ5ǰÙîǰöĊêĞćĒĀîŠÜđðŨîßć÷ĀøČĂĀâĉÜÖĘĕéšǰ2ǰêĞćĒĀîŠÜǰÝĞćîüîüĉíĊìĊęÝąøĆïđךć ìĞćÜćîđìŠćÖĆïǰ 5,2 5! 20 3! P ǰüĉíĊǰ êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ20x12x20 = 4,800ǰüĉíĊ →81 oo - trsenseereenersoooonseo TTTtettnettn-otttettsttttesststr.cn рр COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 4 êĆüĂ÷ŠćÜìĊęǰ8ǰǰÝąÝĆéÙîǰ6 ÙîǰđךćîĆęÜĒëüêøÜǰĔîÖúčŠöîĊĚöĊǰđöêêćĒúąðøćîĊǰøüöĂ÷ĎŠéšü÷ǰÝąÝĆéĕéšÖĊęüĉíĊǰ 1) ëšćđöêêćĒúąðøćîĊ÷ČîêĉéÖĆîđÿöĂ üĉíĊìĞć ĔĀšđöêêćĒúąðøćîĊǰøüöÖúčŠöÖĆîǰĒúšü÷ČîđøĊ÷ÜÿĆïđðúĊę÷îÖĆïđóČęĂîìĊęđĀúČĂìĆĚÜǰǰÙîǰĕéšǰ 5! 120 ǰüĉíĊ đöêêćĒúąðøćîĊǰÿćöćøë÷ČîÿúĆïìĊęÖĆîđĂÜĕéšǰ 2! 2 ǰüĉíĊ êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 2 120 240 u ǰüĉíĊ 2) đöêêćĒúąðøćîĊ÷ČîĕöŠêĉéÖĆî üĉíĊìĞć đîČęĂÜÝćÖÖćøĀćÝĞćîüîüĉíĊìĊęđöêêćĒúąðøćîĊ÷ČîĕöŠêĉéÖĆîîĆĚîǰÝąêšĂÜĒ÷ÖđðŨîÖøèĊĀúć÷ÖøèĊǰ đߊîǰÖøèĊìĊęöĊÙîǰǰÙîĒìøÖǰÙîǰǰÙîĒìøÖǰÙîǰǰÙîĒìøÖëšć÷ĉęÜöĊÝĞćîüîÿĉęÜ×ĂÜĀøČĂÝĞćîüîÙîĔî ēÝì÷ŤöćÖǰÝą÷ĉęÜìĞćĔĀšêšĂÜöĊÖćøĒïŠÜÖøèĊêŠćÜėǰöćÖǰ éĆÜîĆĚîÝċÜĔßšĀúĆÖÖćøÙĂöóúĊđöîêŤöćߊü÷ĔîÖćøÙĞćîüè ÝĞćîüîüĉíĊìĊęÿĉęÜ×ĂÜĕöŠêĉéÖĆîǰ= ÝĞćîüîüĉíĊìĆĚÜĀöéǰıǰÝĞćîüîüĉíĊìĊęÿĉęÜ×ĂÜêĉéÖĆîǰ đøĉęöÝćÖǰĀćÝĞćîüîüĉíĊìĆĚÜĀöéǰÝćÖêĆüĂ÷ŠćÜöĊÙîìĆĚÜĀöéǰǰÙîǰÿćöćøë÷ČîđøĊ÷ÜÿĆïđðúĊę÷îǰĕéšǰ 6! 720 ǰüĉíĊ ÝĞćîüîüĉíĊìĊęÿĉęÜ×ĂÜêĉéÖĆî îĆęîÙČĂǰÝĞćîüîüĉíĊìĊęđöêêćĒúąðøćîĊ÷ČîêĉéÖĆîđÿöĂǰ ÝćÖךĂǰǰĕéš đìŠćÖĆïǰǰüĉíĊ éĆÜîĆĚîǰéĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 720 240 480 ǰüĉíĊ รอ82 าอtarsTาคาารprอจsTTรsาไttTาsนนrrnนาStอหาอไองorงo TT geeesssttttttttttttortesnrsttssae trrsttttstnnsrtnrensstnsttttnsroessstessettssretrnsssttotrnpotrrs рс COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 5 ĒïïòřÖìĆÖþąđóČęĂìéÿĂïÙüćöđךćĔÝìĊęǰ1 ÙĞćßĊĚĒÝÜǰǰĔĀšîĆÖđøĊ÷îĒÿéÜĒîüÙĉéÿĆĚîėđóČęĂĀćÙĞćêĂï 1. ÝÜĀćÝĞćîüîüĉíĊ×ĂÜÖćøìéúĂÜÿčŠöêŠĂĕðîĊĚ 1.1 ÝĆéÙîǰ4 ÙîîĆęÜïîđÖšćĂĊĚ÷ćüǰĕéšÖĊęüĉíĊ [24] 1.2 ÝĆéüćÜĀîĆÜÿČĂǰ7 đúŠöìĊęĒêÖêŠćÜÖĆîïĆîßĆĚîĀîĆÜÿČĂđéĊ÷üÖĆîǰĕéšÖĊęüĉíĊ [5040] 1.3 ÝćÖÖúŠĂÜìĊęöĊúĎÖïĂúĒêÖêŠćÜÖĆîǰ5 úĎÖǰĀ÷ĉïúĎÖïĂúÝĞćîüîǰ5 úĎÖìĊúąúĎÖēé÷ĕöŠĔÿŠÙČîǰĕéšÖĊęüĉíĊ [120] 1.4 ÿøšćÜÙĞć (ēé÷ĕöŠÙĞćîċÜëċÜÙüćöĀöć÷)ǰÝćÖÖćøÿúĆïêĆüĂĆÖþøìčÖêĆüĔîÙĞćüŠćǰIPHONEǰĕéšÖĊęÙĞć [720] 1.5 ÖĞćĀîéĔĀšǰǰA = {1, 2, 3, 4, 5, 6} ÿøšćÜôŦÜÖŤßĆîǰǰf : A o AǰĕéšÖĊęôŦÜÖŤßĆîìĊęđðŨîôŦÜÖŤßĆîǰ1 ı 1 [720] 83 ttttreersrs.sre.oroernsoroe.com oo рт COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 6 1.6 ÝćÖÙîǰ10 ÙîđúČĂÖöćǰ3 ÙîĔĀšêĂïÙĞćëćöìĊęĒêÖêŠćÜÖĆîǰ3 ÙĞćëćöǰĕéšÖĊęüĉíĊ [720] 1.7 öĊ×îöǰ5 ßĉĚîǰîĞćìĆĚÜĀöéĕðĒÝÖĔĀšÖĆïÙîìĊęöĊĂ÷ĎŠǰǰ8 Ùîǰēé÷ĒêŠúąÙîĕéšøĆïĕöŠđÖĉîǰ1 ßĉĚîǰĕéšÖĊęüĉíĊ [6720] 1.8 ÖćøđúČĂÖìĊęîĆęÜ×ĂÜîĆÖđøĊ÷îǰ3 ÙîǰĔîĀšĂÜđøĊ÷îìĊęöĊǰ40 ìĊęîĆęÜǰĕéšÖĊęüĉíĊ [59280] 1.9 ÖćøÿøšćÜøĀĆÿǰ4 êĆüǰēé÷ĒêŠúąĀúĆÖđðŨîđú×ìĊęĒêÖêŠćÜÖĆîǰÝćÖđú×ēééǰ0 ı 9 [5040] 1.10 ÖćøÿøšćÜøĀĆÿǰ4 êĆüǰēé÷ĒêŠúąêĆüđðŨîêĆüĂĆÖþøìĊęĒêÖêŠćÜÖĆîǰÝćÖÙĞćüŠćǰpromotion [840] 84 tttreatrrerrerosootttttrtsstetneooesoeesttreorosrtsern renoeco onesreerentretestetntrrtreotrne nesssnrsttettrttrestsstttstetttntnoenss сй COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 7 ÙĞćßĊĚĒÝÜǰǰĔĀšîĆÖđøĊ÷îĒÿéÜüĉíĊìĞćĂ÷ŠćÜúąđĂĊ÷é . ÖĞćĀîéĔĀšÙøĂïÙøĆüĀîċęÜðøąÖĂïéšü÷ǰóŠĂǰĒöŠǰúĎÖÿćüÙîēêǰúĎÖßć÷ǰ2 ÙîǰĒúąúĎÖÿćüÙîđúĘÖ ëšćÙîìĆĚÜǰ6 ÙîîĊĚîĆęÜïîđÖšćĂĊĚ÷ćüêĆüĀîċęÜǰÝąĕéšÖĊęüĉíĊđöČęĂ .1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉöǰǰ[720] .2 êĞćĒĀîŠÜĀĆüĒëüđðŨîđðŨîđóýßć÷ǰǰ[360] .3 úĎÖßć÷ÿĂÜîĆęÜĕöŠêĉéÖĆîđú÷ [480] .4 óŠĂĒúąĒöŠîĆęÜøĉöÿčéÙîúąéšćî×ĂÜĒëüǰ[48] .5 úĎÖìĆĚÜǰ4 ÙîîĆęÜêĉéÖĆîǰǰ[144] 85 tttttttttttttttttts-eorrnsses-rrsotrnmseaerosgttrttretersss.ee msstne zgetnrfttssorottssres netstetnenrorrsrtrrretrasnnnttinottn ск COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 8 . ÝćÖÙĞćüŠćǰǰspecial îĞćìĆĚÜĀöéöćÿøšćÜđðŨîÙĞćĔĀöŠēé÷ĕöŠÙĞćîċÜëċÜÙüćöĀöć÷ǰǰÝąĕéšÖĊęÙĞćđöČęĂ .1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉö [5040] .2 ÙĞćîĆĚî×ċĚîêšîĒúąúÜìšć÷éšü÷ó÷Ćâßîą [1440] .3 ÙĞćîĆĚîĕöŠöĊó÷ĆâßîąêĉéÖĆî [144] .4 ÙĞćîĆĚîĕöŠöĊÿøąêĉéÖĆîǰĒúąǰĕöŠöĊó÷ĆâßîąêĉéÖĆî [144] .5 ÙĞćîĆĚîöĊÿøąêĉéÖĆîđóĊ÷Üǰ2 êĆüđìŠćîĆĚî [2880] 86 sarntosts ← zesrsrreosroestotttnorroonsrseorost Boronsrrsntttttntrensstnsene с2 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 9 4. öĊîĆÖđøĊ÷îßć÷ǰ2 ÙîǰîĆÖđøĊ÷îĀâĉÜǰ 2 ÙîǰĒúąÙøĎǰ 3 ÙîǰǰÝąöĊüĉíĊÖćøÝĆé÷ČîđøĊ÷ÜĒëüÖĊęüĉíĊǰđöČęĂ 4.1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉö [5040] 4.2 îĆÖđøĊ÷îĀâĉÜ÷ČîêĉéÖĆî [1440] 4.3 ĕöŠöĊÙøĎÙîĔé÷ČîêĉéÖĆî [1440] 4.4 îĆÖđøĊ÷îßć÷ìĆĚÜĀöé÷ČîêĉéÖĆîǰĒêŠĕöŠöĊÙøĎÙîĔé÷ČîêĉéÖĆîǰ [288] 4.5 îĆÖđøĊ÷îßć÷÷ČîêĉéÖĆîǰîĆÖđøĊ÷îĀâĉÜ÷ČîêĉéÖĆîǰĒêŠĕöŠöĊÙøĎÙîĔé÷ČîêĉéÖĆî [48] 87 tdttttteeeoosrsearosttSTDstreoreore.rrrsotttrars.tttne.es nsssnesn rvstttstostttotstn n-stsoTTSTTETT-sr-rtrreorts-ess.ee см COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 10 5. ÝćÖđú×ēééǰ 1, 2, 3, 4, 5, 6 îĞćìĆĚÜĀöéöćÿøšćÜđðŨîÝĞćîüîǰ6 ĀúĆÖ 5.1 ĕöŠöĊđÜČĂîĕ×đóĉęöđêĉö [720] 5.2 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜđðŨîÝĞćîüîìĊęöćÖÖüŠćǰ500,000ǰǰǰ[240] 5.3 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜđðŨîÝĞćîüîÙĎŠ [360] 5.4 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜĕöŠöĊđú×ÙĎŠêĆüĔéĂ÷ĎŠĔîĀúĆÖìĊęêĉéÖĆîđú÷ [144] 5.5 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜöĊđú×ÙĎŠìĆĚÜÿćöêĆüĂ÷ĎŠĔîĀúĆÖìĊęêĉéÖĆî [144] 88 tttthttttttttstrnstsssennssttnsstsstttttattstetottsssrettrs rnsoeoss_rsstttts.essotrr-r tsr-sses.TT?orssETTnttor tnoors сн COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ Part 4ǰÖćøđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜđÿšî ÿĉęÜ×ĂÜàĚĞćÖĆî Linear Permutation COMBINATORIC and PROBABILITY øć÷üĉßćÙĂöïĉîćìĂøĉÖĒúąÙüćöîŠćÝąđðŨî ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰøć÷üĉßćđóĉęöđêĉöÖúčŠöǰ1øĀĆÿüĉßćǰÙ30203 îć÷ïčâđÿøĉåǰǰÝĆîìøŤìĉîǰ ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ǰǰǰǰ ēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ǰîÙøýøĊíøøöøćßÿĞćîĆÖÜćî đ×êóČĚîìĊęöĆí÷öýċÖþćđ×êǰ12ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ Se89 со COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 1 ñúÖćøđøĊ÷îøĎš:: ĒÖšēÝì÷ŤðŦâĀćđÖĊę÷üÖĆïÖćøđøĊ÷ÜÿĆïđðúĊę÷î×ĂÜàĚĞćđßĉÜđÿšîêøÜĕéš üĉíĊđøĊ÷ÜÿĆïđðúĊę÷îĒïïđßĉÜđÿšî×ĂÜÿĉęÜ×ĂÜǰǰ n ÿĉęÜǰìĊęĒêÖêŠćÜÖĆîĕöŠìĆĚÜĀöéÙøćüúąǰ n ÿĉęÜǰ(ēé÷ìĊęĒêŠ úąêĞćĒĀîŠÜĔßš×ĂÜĕöŠàĚĞćÖĆî)ǰàċęÜÖćøĀćÝĞćîüîüĉíĊÖćøÿĆïđðúĊę÷îđðŨîéĆÜîĊĚ ĒîüÙĉéĀúĆÖǰÙČĂÝĆéđøĊ÷ÜĔîúĆÖþèąìĊęÿĉęÜ×ĂÜĒêÖêŠćÜÖĆîìĆĚÜĀöéÖŠĂîǰǰĒúšüĀćøéšü÷ÝĞćîüîÿĉęÜ×ĂÜìĊęàĚĞć ÖĆîđóøćąÖćøÿĆïđðúĊę÷îõć÷ĔîÖúčŠöÿĉęÜ×ĂÜìĊęđĀöČĂîÖĆîĕöŠöĊÙüćöÿĞćÙĆâĀøČĂĕöŠêŠćÜÖĆî êĆüĂ÷ŠćÜìĊęǰǰǰêšĂÜÖćøÙîÜćîǰ6 ÙîǰĔĀšéĎĒúÙüćöÿąĂćé×ĂÜēøÜđøĊ÷îĒĀŠÜĀîċęÜǰÝąöĊüĉíĊìĆĚÜĀöéÖĊęüĉíĊǰëšć ÖĞćĀîéĔĀšĂćÙćøĀúĆÜìĊęǰ1 öĊÙîÜćîǰ3 ÙîǰĂćÙćøĀúĆÜìĊęǰ2 öĊÙîÜćîǰ2 ÙîǰĒúąĂćÙćøĀúĆÜìĊęǰ3 öĊ ÙîÜćîǰ1 Ùî üĉíĊìĞćǰǰǰǰǰÝĞćîüîüĉíĊìĊęÝąÝĆéÙîÜćîǰ6 ÙîǰĂĂÖđðŨîǰ3 ÖúčŠö ǰÖúčŠöĒøÖĂ÷ĎŠĂćÙćøĀúĆÜìĊęǰ1 öĊĕéš 3 Ùî ǰÖúčŠöìĊęÿĂÜĂ÷ĎŠĂćÙćøĀúĆÜìĊęǰ2 öĊĕéš 2 Ùî ǰÖúčŠöìĊęÿćöĂ÷ĎŠĂćÙćøĀúĆÜìĊęǰ3 öĊĕéš 1 Ùî êĂïǰÝĞćîüîüĉíĊìĊęÝąÝĆéÙîÜćîĕéšìĆĚÜĀöéǰǰ 6! 3!2!1!ǰǰ ǰǰ60 ǰüĉíĊ ÖćøđøĊ÷ÜÿĆïđðúĊę÷î×ĂÜìĊęĕöŠĒêÖêŠćÜÖĆî ×ĂÜàĚĞćǰđßĉÜđÿšîêøÜǰǰ ǰǰǰǰ ÝĞćîüîǰ2 Ùćï ëšćöĊÿĉęÜ×ĂÜĂ÷ĎŠǰǰ n ÿĉęÜǰǰìĊęĒêÖêŠćÜÖĆîĕöŠìĆĚÜĀöéǰǰēé÷ìĊę ǰǰ ĔîÖúčŠöìĊęǰ 1 ǰǰöĊÿĉęÜ×ĂÜàĚĞćÖĆîǰǰǰ 1 n ǰǰÿĉęÜ ĔîÖúčŠöìĊęǰ 2 ǰǰöĊÿĉęÜ×ĂÜàĚĞćÖĆîǰǰǰ 2 n ǰǰÿĉęÜ ĔîÖúčŠöìĊęǰ k ǰǰöĊÿĉęÜ×ĂÜàĚĞćÖĆîǰǰǰ k n ǰǰÿĉęÜ Ēúą 1 n + 2 n ļ k n = n ÝąĕéšÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷î×ĂÜÿĉęÜ×ĂÜìĆĚÜǰǰ n ÿĉęÜǰđìŠćÖĆïǰǰǰ 1 2 ! ! !... ! k n nn n üĉíĊ 90 ottttettttrrsrrostettstensrsrnsrterettrerersrrsresrnsste Bs rssesttssetssosrotooonsetoae osrfttesostereseettonosste с6 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 2 êĆüĂ÷ŠćÜ 2 öĊÙĎðĂÜúéøćÙćǰ20% 15% Ēúąǰ10% ÝĞćîüîǰǰ2 Ĕïǰǰ3 ĔïǰĒúąǰǰ5 ĔïǰêćöúĞćéĆïǰ îĞćÙĎðĂÜìĆĚÜĀöéîĊĚĒÝÖĔĀšÖĆïđóČęĂîėǰ10 ÙîǰÙîúąǰ1 ĔïÝąöĊüĉíĊÖćøĒÝÖĕéšÖĊęüĉíĊ üĉíĊìĞć ÝĞćîüîüĉíĊìĊęÝąĒÝÖÙĎðĂÜĔĀšÖĆïđóČęĂîǰǰÙîǰĂĂÖđðŨîǰ3 ÖúčŠö ǰÖúčŠöĒøÖÙĎðĂÜúéøćÙćǰ% öĊ Ĕï ǰÖúčŠöìĊęÿĂÜÙĎðĂÜúéøćÙćǰ% öĊ Ĕï ǰÖúčŠöìĊęÿćöÙĎðĂÜúéøćÙćǰ% öĊ Ĕï êĂïǰÝĞćîüîüĉíĊìĊęÝąĒÝÖÙĎðĂÜĔĀšÖĆïđóČęĂîǰǰÙîǰĕéšìĆĚÜĀöéǰǰ 10! 2!3!5!ǰǰ ǰǰ2,520 ǰüĉíĊ êĆüĂ÷ŠćÜìĊęǰ3ǰǰßć÷ÙîĀîċęÜêšĂÜÖćøđéĉîĕðëċÜÝčéìĊęĀŠćÜÝćÖÝčéđøĉęöêšîĕðךćÜĀîšćǰǰÖšćüǰēé÷ìĊęÿćöćøë ÖšćüĕðךćÜĀîšćĀøČĂëĂ÷ĀúĆÜÖĘĕéšǰĒêŠöĊđÜČęĂîĕ×üŠćÝąêšĂÜđéĉîøüöÖĆîĒúšüĕéšǰǰÖšćüǰÝÜĀćüŠćđ×ćÝąđéĉî ĕéšÖĊęüĉíĊ üĉíĊìĞć ĔĀšǰ F ǰĒìîÖćøÖšćüđéĉîĕðךćÜĀîšć×ĂÜßć÷ÙîîĊĚ ǰǰǰǰ B ǰĒìîÖćøÖšćüđéĉîëĂ÷ĀúĆÜ×ĂÜßć÷ÙîîĊĚ ìčÖėÙøĆĚÜ×ĂÜÖćøđéĉî×ĂÜßć÷ÙîîĊĚđóČęĂĔĀšÖšćüđéĉîÝîÙøïǰǰÖšćüǰĒúąđéĉîĕðëċÜÝčéìĊęĀŠćÜÝćÖ ÝčéđøĉęöêšîĕðךćÜĀîšćǰǰÖšćüǰÝąóïüŠćǰêšĂÜđéĉîĕðךćÜĀîšćǰǰÖšćüǰĒúąđéĉîëĂ÷ĀúĆÜǰǰÖšćüǰđÿöĂ éĆÜîĆĚîÝĞćîüîüĉíĊìĊęßć÷ÙîîĊĚÝąđéĉîĕéšǰđìŠćÖĆïǰ 10! 120 7!3! ǰüĉíĊ êĂï ǰüĉíĊ êĆüĂ÷ŠćÜìĊęǰ4ǰǰîĞćĂĆÖþøÝćÖÙĞćüŠćǰALGEBRA öćđøĊ÷ÜÿĆïđðúĊę÷îĕéšÖĊęĒïïǰëšćêšĂÜøĆÖþćúĞćéĆï×ĂÜÿøą Ēúąó÷ĆâßîąĔĀšđðŨîĒïïđéĉö üĉíĊìĞć ĔîÙĞćüŠćǰALGEBRAǰúĞćéĆïÖćøđøĊ÷Ü×ĂÜó÷ĆâßîąĒúąÿøąđðŨî ÿøąǰó÷Ćâßîąǰó÷Ćâßîąǰÿøąǰó÷Ćâßîąǰó÷Ćâßîąǰÿøąǰǰ ÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îó÷Ćâßîąĕéšǰ 4! 24 üĉíĊ ÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îÿøąĕéšǰ 3! 2! 3 üĉíĊ êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 3 24 72 u ǰüĉíĊ êĆüĂ÷ŠćÜìĊęǰǰǰÝÜĀćÝĞćîüîüĉíĊìĊęÝąÝĆéđú×ēééìĆĚÜǰ6 êĆüĔîǰ556667 ĔĀšĕéšÝĞćîüîìĊęöĊĀÖĀúĆÖêŠćÜėÖĆî üĉíĊìĞć ĔîÖćøÝĆéđú×ēééìĆĚÜǰǰêĆüǰĔîǰǰàċęÜĒïŠÜđðŨîǰ đú×ēééǰǰöĊÝĞćîüîǰǰêĆü đú×ēééǰǰöĊÝĞćîüîǰǰêĆü đú×ēééǰǰöĊÝĞćîüîǰǰêĆü êĂï éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 6! 3!2!1!ǰǰ ǰǰ60 ǰüĉíĊ 91 tttdasoosotteessrsstrnseeestttrertsotosottetntsoentnte RT wttrttntrssttttp osoesstostoetttssstentttttttttrg ср COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 3 êĆüĂ÷ŠćÜǰ öĊĀîĆÜÿČĂüĉßćüĉì÷ćýćÿêøŤđĀöČĂîÖĆîǰ3 đúŠöǰĀîĆÜÿČĂüĉßćõćþćĂĆÜÖùþìĊęđĀöČĂîÖĆîĂ÷ĎŠǰǰǰǰ 2 đúŠöǰĀîĆÜÿČĂüĉßćÿĆÜÙöìĊęđĀöČĂîÖĆîǰ3 đúŠöǰĒúąüĉßćÙèĉêýćÿêøŤìĊęêŠćÜÖĆîĂĊÖǰ2 đúŠöǰÝąöĊüĉíĊÝĆé ĀîĆÜÿČĂǰ10 đúŠöîĊĚđøĊ÷ÜêĉéêŠĂÖĆîïîßĆĚîĀîĆÜÿČĂĕéšÖĊęüĉíĊ (1) ĀîĆÜÿČĂđúŠöĔéĂ÷ĎŠìĊęĔéÖĘĕéš (2) ĀîĆÜÿČĂüĉßćđéĊ÷üÖĆîĂ÷ĎŠêĉéÖĆî (3) ĕöŠöĊĀîĆÜÿČĂüĉßćÙèĉêýćÿêøŤĂ÷ĎŠêĉéÖĆîǰ (4) ĕöŠöĊĀîĆÜÿČĂÿĆÜÙöÿĂÜđúŠöĔéĂ÷ĎŠêĉéÖĆî üĉíĊìĞć (1)ǰĀîĆÜÿČĂđúŠöĔéĂ÷ĎŠìĊęĔéÖĘĕéšöĊĀîĆÜÿČĂìĆĚÜĀöéǰǰđúŠöǰēé÷ĒïŠÜđðŨîüĉì÷ćýćÿêøŤ đĀöČĂîÖĆîǰ3 đúŠöǰĀîĆÜÿČĂüĉßćõćþćĂĆÜÖùþìĊęđĀöČĂîÖĆîĂ÷ĎŠǰ2 đúŠöǰĀîĆÜÿČĂüĉßćÿĆÜÙöìĊęđĀöČĂîÖĆîǰ3 đúŠöǰĒúąüĉßćÙèĉêýćÿêøŤìĊęêŠćÜÖĆîĂĊÖǰ2 đúŠöǰéĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 10! 3!2!3!1!1! ǰǰ420 üĉíĊ (2)ǰĀîĆÜÿČĂüĉßćđéĊ÷üÖĆîĂ÷ĎŠêĉéÖĆîǰöĊĀîĆÜÿČĂìĆĚÜĀöéǰǰđúŠöǰēé÷ĒïŠÜđðŨîüĉì÷ćýćÿêøŤ đĀöČĂîÖĆîǰ3 đúŠöǰ öĆéêĉéÖĆîǰĀîĆÜÿČĂüĉßćõćþćĂĆÜÖùþìĊęđĀöČĂîÖĆîĂ÷ĎŠǰ2 đúŠöǰ öĆéêĉéÖĆîǰĀîĆÜÿČĂüĉßć ÿĆÜÙöìĊęđĀöČĂîÖĆîǰ3 đúŠöǰ öĆéêĉéÖĆîǰĒúąüĉßćÙèĉêýćÿêøŤìĊęêŠćÜÖĆîĂĊÖǰ2 đúŠö öĆéêĉéÖĆî ÝċÜöĊĀîĆÜÿČĂìĊęöĆéêĉéÖĆîĒúšüìĆĚÜĀöéÙĉéđðŨîǰǰÖúčŠöǰÝćÖîĆĚîÝċÜîĞćìĆĚÜǰǰÖúčŠöîĊĚǰđøĊ÷Ü ÿĆïđðúĊę÷îÖĆîǰēé÷ǰǰĔîǰǰÖúčŠöîĊĚǰđðŨîĀîĆÜÿČĂÙèĉêýćÿêøŤìĊęêŠćÜÖĆîǰÝċÜÿćöćøëđøĊ÷ÜÿĆïđðúĊę÷îÖĆîĕéšǰ éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 4! 2! 24 2 48 u u ǰüĉíĊ (3) ĕöŠöĊĀîĆÜÿČĂüĉßćÙèĉêýćÿêøŤĂ÷ĎŠêĉéÖĆîǰîĞćĀîĆÜÿČĂìĆĚÜǰǰđúŠöǰ ĕöŠîĆïøüöÙèĉêýćÿêøŤ ìĊęĒêÖêŠćÜÖĆîǰǰđúŠöǰđøĊ÷ÜÿĆïđðúĊę÷îÖĆîǰĒúšüÝċÜîĞćÙèĉêýćÿêøŤìĊęĒêÖêŠćÜÖĆîìĆĚÜǰǰđúŠöǰĒìøÖēé÷ ĕöŠĔĀšêĉéÖĆîǰ üĉì÷Ť ǰüĉì÷Ťǰ üĉì÷Ťǰ ĂĆÜÖùþǰ ĂĆÜÖùþǰ ÿĆÜÙöǰ ÿĆÜÙö ǰÿĆÜÙö éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 9,2 8! 40,320 9 8 120,960 3!2!2! u uu P ǰüĉíĊ (4) ĕöŠöĊĀîĆÜÿČĂÿĆÜÙöÿĂÜđúŠöĔéĂ÷ĎŠêĉéÖĆî îĆęîÙČĂǰĀîĆÜÿČĂÿĆÜÙöìĆĚÜÿćöđúŠöĂ÷ĎŠĒ÷ÖÖĆî ìĆĚÜĀöéǰîĞćĀîĆÜÿČĂìĆĚÜǰǰđúŠöǰ ĕöŠîĆïøüöÿĆÜÙöìĊęđĀöČĂîÖĆîǰǰđúŠöǰđøĊ÷ÜÿĆïđðúĊę÷îÖĆîǰĒúšüÝċÜîĞćÿĆÜÙö ìĊęđĀöČĂîÖĆîǰǰđúŠöǰĒìøÖēé÷ĕöŠĔĀšêĉéÖĆî ǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰüĉì÷Ť ǰüĉì÷Ťǰ üĉì÷Ťǰ ĂĆÜÖùþǰ ĂĆÜÖùþǰ Ùèĉêǰ Ùèĉê éĆÜîĆĚîÝĞćîüîüĉíĊìĆĚÜĀöéđìŠćÖĆïǰ 7! 8,3 420 56 23,520 2!3!1!1! 3! P u u ǰüĉíĊ üĉì÷Ťǰüĉì÷Ťǰüĉì÷Ť ĂĆÜÖùþǰĂĆÜÖùþ ÿĆÜÙöǰÿĆÜÙöǰÿĆÜÙö ÙèĉêǰǰÙèĉêǰ 92 nttstoevssrnssrssssrerossotfooooerngrraesrettre naosssy - motostntnensrnnoorosersnsosrre nrertsttsstsossnserssrest сс COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 4 ĒïïòřÖìĆÖþąđóČęĂìéÿĂïÙüćöđךćĔÝìĊęǰ1 ÙĞćßĊĚĒÝÜǰǰĔĀšîĆÖđøĊ÷îĒÿéÜĒîüÙĉéÿĆĚîėđóČęĂĀćÙĞćêĂï 1. ÝÜĀćÝĞćîüîüĉíĊ×ĂÜÖćøìéúĂÜÿčŠöêŠĂĕðîĊĚ 1.1 ÖćøÝĆéđøĊ÷ÜÿĆïđðúĊę÷îêĆüĂĆÖþøìĆĚÜĀöéÝćÖÙĞćüŠć LEVEL ĔĀšđðŨîÙĞćìĊęĕöŠÙĞćîċÜëċÜ ÙüćöĀöć÷ĕéšÖĊęÙĞć [30] 1.2 ÖćøÝĆéđøĊ÷ÜÿĆïđðúĊę÷îêĆüĂĆÖþøìĆĚÜĀöéÝćÖÙĞćüŠć COFFEE ĔĀšđðŨîÙĞćìĊęĕöŠÙĞćîċÜëċÜ ÙüćöĀöć÷ĕéšÖĊęÙĞć [180] 1.3 ÿøšćÜÝĞćîüîǰ6 ĀúĆÖÝćÖđú×ēééìĆĚÜ 6 êĆüÙČĂǰ1, 2, 2, 3, 3, 3 ĕéšÖĊęÝĞćîüî [60] 1.4 ÿøšćÜÝĞćîüîǰ5 ĀúĆÖÝćÖđú×ēééìĆĚÜǰ5 êĆüÙČĂǰ2, 2, 2, 3, 3 ĕéšÖĊęÝĞćîüî [10] 1.5 ÙøĂïÙøĆüìĊęÝąöĊúĎÖßć÷ǰ3 ÙîǰĒúąúĎÖÿćüǰ2 ÙîǰöĊìĆĚÜĀöéÖĊęüĉíĊ (øĎðĒïï) [10] 93 rttttttthtttsstesrssensstespeoesrttatttshehrsrrpeosssrrsrrosrtte norot serrssstsrsranretosttstttreen gesrstsststtttnssstssrnesrtstnorooeeonostnsossemttrm ст COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 5 ÝĆéđøĊ÷ÜÿĆïđðúĊę÷îêĆüĂĆÖþøìĆĚÜĀöéĔîÙĞćüŠćǰMESSENGER ēé÷ìĊę×ċĚîêšîéšü÷ǰM ĒúąǰĕöŠöĊ ĂĆÖþøǰE êĆüĔéêĉéÖĆîđú÷ǰĕéšìĆĚÜĀöéÖĊęÙĞćìĊęĕöŠÙĞćîċÜëċÜÙüćöĀöć÷ǰ<> ÿøšćÜÝĞćîüîǰǰĀúĆÖÝćÖđú×ēééǰ, , , , , , ǰǰĕéšÖĊęÝĞćîüîđöČęĂđú×ǰǰêĉéÖĆîǰ<> 1.8 öĊđÿČĚĂÿĊéĞćìĊęđĀöČĂîÖĆîǰ3ǰêĆüǰĒúąÿĊ×ćüìĊęđĀöČĂîÖĆîǰ2ǰêĆüǰîĞćìĆĚÜĀöéĕðĒÝÖđéĘÖǰ5ǰÙîė úąêĆüĕéšÖĊęüĉíĊǰ<10] 1.9 öĊđÙšÖìĊęđĀöČĂîÖĆîǰ4ǰßĉĚîǰÙčÖÖĊĚìĊęđĀöČĂîÖĆîǰ3ǰëčÜǰĒúąđàîüĉßìĊęđĀöČĂîÖĆîǰ2ǰßĉĚîǰǰ îĞćìĆĚÜĀöéĕðĒïŠÜđóČęĂîǰ9 ÙîėúąǰßĉĚî ÙîúąëčÜǰĕéšÖĊęüĉíĊǰǰ<1260] 1.10 ëšćêšĂÜÖćøìćÿĊéĞćĒúąÿĊ×ćüúÜĔîߊĂÜïîĒñŠîüÜÖúöìĊęöĊǰ8 ߊĂÜǰìčÖߊĂÜǰēé÷ìćÿĊéĞćǰ6 ߊĂÜǰÝąöĊÖĊęüĉíĊǰ<28] 94 tettttttttensoosstssttnttsttttststttttttttsoorssttesra sesrsoootottttottostttrnsrtsstt nrsottressoosttossestttstttrttttr тй COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 6 ÙĞćßĊĚĒÝÜǰǰĔĀšîĆÖđøĊ÷îĒÿéÜüĉíĊìĞćĂ÷ŠćÜúąđĂĊ÷é 2. ÝćÖÙĞćüŠćǰBANANA îĞćêĆüĂĆÖþøìĆĚÜĀöéöćđøĊ÷ÜđðŨîÙĞćēé÷ĕöŠÙĞćîċÜëċÜÙüćöĀöć÷ÝąĕéšÖĊęÙĞćđöČęĂ 2.1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉö [60] 2.2 ĕöŠöĊêĆüĂĆÖþøǰA êĉéÖĆî [12] 2.3 ĕöŠöĊêĆüĂĆÖþøǰN êĉéÖĆî [40] 2.4 ×ĆĚîêšîéšü÷ó÷ĆâßîąǰĒúąĂĆÖþøǰA ĕöŠêĉéÖĆî [3] 2.5 ĂĆÖþøǰA êĉéÖĆîđóĊ÷Ü 2 êĆüđìŠćîĆĚî [36] 95 tttTTt.treet.ee#trsssTsSreeoesersrrssEpspftpopfcengEeTG-.nsT'DeerotttreT oootttetoststtttnersesrrsetotnn тк COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 7 3. ÝćÖđú×ēééǰǰ1, 1, 1, 2, 2, 3, 3 îĞćìĆĚÜĀöéöćÿøšćÜđðŨîÝĞćîüîǰ7 ĀúĆÖǰǰÝąĕéšÖĊęÝĞćîüîđöČęĂ 3.1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉö [210] 3.2 ÝĞćîüîìĊęÿøšćÜđðŨîÝĞćîüîÙĊę [150] 3.3 ÝĞćîüîìĊęÿøšćÜđðŨîÝĞćîüîÙĎŠ [60] 3.4 ÝĞćîüîìĊęÿøšćÜđðŨîÝĞćîüîìĊęöćÖÖüŠćǰ2 úšćî [120] 3.5 ÝĞćîüîìĊęÿøšćÜĀćøéšü÷ǰ4 úÜêĆü [50] 96 tettsernsrersstnsssrnsossssereersesrn eso ossoosttntrsrssrtesttte rettonrssrtnsreossstttsrossssstttttts т2 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 8 4. ÝćÖđú×ēééǰ 0 , 3 , 4 , 4 , 5 , 5 îĞćìĆĚÜĀöéöćÿøšćÜđðŨîÝĞćîüîǰǰ6 ĀúĆÖǰǰÝąĕéšÖĊęÝĞćîüîđöČęĂ 4.1 ĕöŠöĊđÜČęĂîĕ×đóĉęöđêĉö [150] 4.2 ÝĞćîüîìĊęÿøšćÜđðŨîÝĞćîüîÙĊę [72] 4.3 ÝĞćîüîìĊęÿøšćÜđðŨîÝĞćîüîÙĎŠ [78] 97 tttttttttreneonssrresoeesotttertrrssrenrstrrsssottsonsstosre sstte ootsoroereeoterottttttttres tostttttttttnottheertttttttsttns тм COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćǰÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰǰ Ù30203ǰǰǰ ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤǰǰǰǰǰǰǰǰǰǰǰǰǰǰǰ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ 10 5. ÝćÖđú×ēééǰ 1, 2, 3, 4, 5, 6 îĞćìĆĚÜĀöéöćÿøšćÜđðŨîÝĞćîüîǰ6 ĀúĆÖ 5.1 ĕöŠöĊđÜČĂîĕ×đóĉęöđêĉö [720] 5.2 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜđðŨîÝĞćîüîìĊęöćÖÖüŠćǰ500,000ǰǰǰ[240] 5.3 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜđðŨîÝĞćîüîÙĎŠ [360] 5.4 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜĕöŠöĊđú×ÙĎŠêĆüĔéĂ÷ĎŠĔîĀúĆÖìĊęêĉéÖĆîđú÷ [144] 5.5 ÝĞćîüîǰ6 ĀúĆÖìĊęÿøšćÜöĊđú×ÙĎŠìĆĚÜÿćöêĆüĂ÷ĎŠĔîĀúĆÖìĊęêĉéÖĆî [144] 88 ส"างไ& 6 ! = 720 '( i. ส"าง )นวน 6 ห-กไ& 720 '( * -5 e- nrn e- emr -5 ห-ก แสน0เ2นไปไ& 4อ 5,6 i. 6ดไ& 2 ✗ 5 ! = 240 '( # ห-กห8วย0 เ2นไปไ& = 2 ,4,6 5 ✗ 4 × 3×2×1×3 = 360 '( # เลข< ; า , 3,5 เลข= i 2 , 4,6 i. 6ด เลข<ไ& 3 ! = 6 '( เลข= แทรกไ& a @แห8ง i. 6ดไ& A = 24 '( i. 6ดไ& 2ค × 6 = แก '( * 1 3 5 2 86 i. 6ดไ& a ! × 3 ! = 24×6=144 '( # ttttreteosesetosooenpreeosstern ☆ tttteosrrokn aoersreesosrroseoeeesttsttttteersrrrrgrrssrerettttttt ornsststtrasoae nerostttrssenoretroneroestnsettrerrosrssrsse rostsetnstettttttrnsrorerns.rs ลอคBsรนอsร* tettnsrosotsstnrsestssrsrrssrsosons Bออคsoa> nereosttttrrtnsrertretef mosstatsrererettteotrtrrssottstesrtttsttnsaonoss тн COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
Part 5ǰÖćøđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜüÜÖúö circular permutation COMBINATORIC and PROBABILITY øć÷üĉßćÙĂöïĉîćìĂøĉÖĒúąÙüćöîŠćÝąđðŨî øć÷üĉßćđóĉęöđêĉöÖúčŠöǰ1øĀĆÿüĉßćǰÙ30203 îć÷ïčâđÿøĉåǰǰÝĆîìøŤìĉîǰ ēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ǰîÙøýøĊíøøöøćßÿĞćîĆÖÜćî đ×êóČĚîìĊęöĆí÷öýċÖþćđ×êǰ12 ss98 то COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD
ÖúčŠöÿćøąÖćøđøĊ÷îøĎšÙèĉêýćÿêøŤ ÖúčŠöēøÜđøĊ÷îüĉì÷ćýćÿêøŤÝčāćõøèøćßüĉì÷ćúĆ÷ đĂÖÿćøðøąÖĂïÖćøđøĊ÷îøĎšǰøć÷üĉßćÙĂöïĉîćìĂøĉÖĒúąÙüćöîŠćÝąđðŨîđïČĚĂÜêšîǰÙ Āîšćǰ1 A C B A B C ÖćøđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜüÜÖúö (Circular Permutation) ÝĞćîüîǰǰÙćï üĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜüÜÖúöǰ Circular permutations) đðŨîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îìĊęÙĞćîċÜëċÜêĞćĒĀîŠÜĔîÖćøüćÜ ÿĉęÜ×ĂÜđߊîđéĊ÷üÖĆïüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜđÿšîǰĒêŠüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜüÜÖúöÝąĕöŠöĊêĞćĒĀîŠÜĀĆüĒëüĀøČĂìšć÷ĒëüǰĀøČĂ ÖúŠćüĕéšüŠćĀćÖđúČĂÖêĞćĒĀîŠÜĔéđðŨîĀĆüĒëüĒúšüêĞćĒĀîŠÜîĆĚîëČĂüŠćđðŨîìšć÷Ēëüéšü÷ǰàċęÜĒêÖêŠćÜÝćÖÖćøđøĊ÷ÜÿĆïđðúĊę÷î đßĉÜđÿšîêøÜǰđߊî ÖćøÝĆéÙîîĆęÜøĂïēêŢąÖúöǰÖćøøšĂ÷óüÜöćúĆ÷đðŨîüÜÖúöǰđðŨîêšîǰîĆÖđøĊ÷îóĉÝćøèćêĆüĂ÷ŠćÜÖćø ÝĆéđøĊ÷ÜéĆÜêŠĂĕðîĊĚ ÿööêĉüŠćöĊêĆüĂĆÖþøìĊęĒêÖêŠćÜÖĆîǰ3ǰêĆüǰĔîìĊęîĊĚÙČĂǰA, B ĒúąǰC ëšćîĞćêĆüĂĆÖþøìĆĚÜÿćöîĊĚöćđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜ đÿšîêøÜÝąĕéšÝĞćîüîüĉíĊìĆĚÜĀöéǰ3! = 6 üĉíĊǰéĆÜêŠĂĕðîĊĚ ABC BCA CAB ACB BAC CBA ĒêŠëšćîĞćêĆüĂĆÖþøǰA, B ĒúąǰCǰöćÝĆéđøĊ÷ÜđðŨîĒïïüÜÖúöÝąÝĆéĕéšéĆÜîĊĚ ÝćÖÖćøüćÜǰA, B ĒúąǰC ìĆĚÜǰ6 õćóךćÜêšîǰóïüŠćǰöĊüĉíĊĒêÖêŠćÜÖĆîđóĊ÷Üǰ2 üĉíĊđìŠćîĆĚîÙČĂ ABC, BCA, CAB ëČĂđðŨîÖćøÝĆéđøĊ÷ÜđéĊ÷üÖĆî ACB, BAC, CBA ëČĂđðŨîÖćøÝĆéđøĊ÷ÜđéĊ÷üÖĆî ÿćöćøëÿĆÜđÖêĕéšÝćÖÖćøđøĊ÷Ü×ĂÜĂĆÖþøǰA, B ĒúąǰCǰüŠćêĆüĂĆÖþøĔéĂ÷ĎŠàšć÷ĀøČĂ×üćÖĆî×ĂÜĒêŠúąøĎðÖĘÝą ìøćïǰîĆęîÙČĂÖćøđøĊ÷ÜÿĆïđðúĊę÷îǰA, B ĒúąǰCǰĔîĒïïüÜÖúöÝąÝĆéĕéšđóĊ÷Üǰ2 üĉíĊ đøćóïüŠćǰÝćÖÝĞćîüîüĉíĊđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜđÿšî×ĂÜÿĉęÜ×ĂÜìĊęĒêÖêŠćÜÖĆîǰǰÿĉęÜǰđöČęĂîĞćöćđøĊ÷ÜđðŨîüÜÖúöǰ đîČęĂÜÝćÖĔîǰǰüĉíĊ×ĂÜÖćøđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜđÿšîǰîĞćöćđøĊ÷ÜÿĆïđðúĊę÷îđßĉÜüÜÖúöĕéšǰǰüĉíĊ àċęÜöĊÙŠćđìŠćÖĆïǰ 3 P 3,3 = 3 !3 = 2! = (3 ı 1)! = 2 üĉíĊ A C B B A C C B A A B C B C A C A B A C B A B C 99 т6 COMBINATORIC AND PROBABILITY>>>>>>>>>>>KRU BIRD