M 14 排列组合

庄老师 018-3801692 奥林匹克数学 Math Olympiad

Name:________________ Date:____________

排列组合

1. 从 0，1，2，3，4，5 这 6 个数字中任意选两个不同的数字组成两位数，那
么在这些两位数中，偶数有多少个？
Choose two different numbers from the 6 numbers 0, 1, 2, 3, 4 and 5 to form a
two-digit number. Then, among these two-digit numbers, how many even
numbers are there?

2. 由数字 0，1，3，9 可以组成多少个四位数？
How many four-digit numbers can be composed of the numbers 0, 1, 3 and 9?

3. 由数字 0，1，3，9 可以组成多少个没有重复数字的数？
How many numbers without repeating numbers can be composed of the
numbers 0, 1, 3 and 9?

4. 用 2，0，1，7 这四个数字可以组成多少个没有重复数字的四位偶数？
How many hour-digit even numbers without repeating numbers can be
composed of the four numbers 2, 0, 1 and 7?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

5. 由数字 0，1，2，3，4 组成一个数
A number composed of the numbers 0, 1, 2, 3, 4
a. 可组成多少个不相同的三位数？

How many different three-digit numbers can be formed?

b. 可组成多少个没有重复数字的三位偶数？
How many three digit even numbers without repeating numbers can be
formed?

6. 用 0，1，2，3，4，5 组成各个数字都不相同的六位数，并把这些六位数从

小到大排列，第 598 个数是多少？
Use 0, 1, 2, 3, 4, 5 to form six-digits with different numbers, and arrange these
six-digit from smallest to largest. What is the 598th number?

7. 用 2，0，1，6 组成的没有重复数字的两位数的平均数是多少？
What is the average of two digits composed of 2, 0, 1 and 6 without repeating
numbers?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

8. 有 4 个球队进行单循环赛，每个队都与其他各队都比赛 1 场，那么这次球赛
一共会有多少场？
There are 4 teams in a single round- robin match and each team competes with
each other. How many matches will there be in total?

9. 学校进行乒乓球比赛，每个选手都要和其他选手赛一场，一共进行了 78 场

比赛，有多少人参加了选拔赛？

The school held a table tennis competition. Each player had to compete with
other players. There were 78 games in total. How many people participated in
the trials?

10. 有 13 队参加篮球赛，比赛分为两个组，第一组 7 个队，第二组 6 个队，各

组先进行单循环赛（即每队都要与其他个队比赛一场），然后由各组的前两

名共 4 队分成两组进行淘汰赛，最后两队决出冠亚军，问共需比赛多少场？
There are 13 teams participating in the basketball game. The competition is
divided into two groups, the first group has 7 teams, and the second group has 6
teams. Each group will have a single round robin(that is each team will have to
play against other teams), and when the top two teams in each group will be
divided into two groups for the elimination rounds. The final two teams will
decide the championship and the runner-up. How many games are needed?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

11. 斑马，长颈鹿，小象，梅花鹿站成一排照相，小象要站在从左往右数的第 2

个，一共有多少种排法？请一一写出。

Zebra, giraffe, elephant and deer stand in a row to take picture. Elephant wants
to stand in the second place from left to right. How many arrangements are
there? List out the arrangements.

12. 小明給四个同学写信，由于粗心，把信装错了信封，结果四个同学都没有收

到写给本人的信，造成这一情况的装信封的方法共有多少种？

MENG wrote to four class mates. Due to his carelessness, e put the letter in the
wrong envelope. As a result, none of the four classmates received the letter
addressed to him. How many ways are there to put the envelope in this
situation?

13. 商店里有 2 种巧克力糖：牛奶味，榛仁味；有三种水果糖：苹果味、梨味、
橙味。小明想买一些糖送给他的朋友。
There are two types of chocolate candies in the store: milk flavor and hazelnut
flavor; and three types of fruit candies: apple flavor, pear flavor and orange
flavor. MENG wants to buy some candy for his friend.
a. 如果小明只想买一种糖，他有多少种选法？
If MENG only wants to buy one kind of candy, how many choices does he
have?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

b. 如果小明想买水果糖、巧克力糖各 1 中，他有多少种选法？
If MENG wants to buy one fruit candy and one chocolate candy, how many
options does he have?

14. 小明有 3 本不同的漫画书，4 本不同的童话书，他想从这些书中选出漫画书
与童话书各一本送给他的朋友小刚。他有多少种送法？
MENG has 3 different comic books and 4 different fairy tale books. He wants to
choose one comic book and one fairy tale book from these books and give them
to his friend GON. How many ways he can send?

15. 用 4 种颜色笔给“MATHS”每个字母涂颜色，要求不同字母用不同颜色的笔去
涂，共有多少种不同的颜色搭配？
Use 4 colour pencil to colour each letter of “MATHS”. Different letters are
required to be painted with different colour pencil. How many different colour
combinations are there?

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庄老师 018-3801692 奥林匹克数学 Math Olympiad

16. 用 10 种颜色笔给“MATHEMATICS”每个字母涂颜色，要求不同字母用不同颜

色的笔去涂，相同的字母用相同的颜色涂，共有多少种不同的颜色搭配？

Use 10 colour pencil to colour each letter of “MATHEMATICS”. Different letters
are required to be painted with different colour pencil and the same letter should
be painted with the same colour. How many different colour combinations are
there?

17. 小明把红、黄、蓝 3 面小旗从上到下挂在竖立的旗杆上代表不同的信号。每
次可以任意挂 1 面、2 面或 3 面。不同的顺序代表不同的信号。一共可以表

示多少种不同的信号？

MENG hung three small flags, red, yellow and blue, from top to bottom on the
erect flag poles to represent different signals. He can hang 1 flag, 2 flag and 3
flags at any time. Different orders represent different signals. How many
different signals can be represented in total?

18. 小明把红、黄、蓝和绿 4 面小旗中的其中 3 面从上到下挂在竖立的旗杆上代
表不同的信号。每次可以任意挂 1 面、2 面或 3 面。不同的顺序代表不同的

信号。一共可以表示多少种不同的信号？

MENG hung three of the four small flags of red, yellow, blue and green from top
to bottom on the erect flag poles to represent different signals. He can hang 1
flag, 2 flag and 3 flags at any time. Different orders represent different signals.
How many different signals can be represented in total?

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