JDM CHAP 7 Combine

Unit Matematik

Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia

JOM-DO-MATHS (JDM)
Chapter 7 Permutations and Combinations( Set 1 )

1. How many ways can 2 alphabets be arranged from word THINKING

2. From the word TRIANGLES, in how many five-letter words can be formed if
a) there is no restriction.
b) the words must be ended with G.
c) there is no vowel in the arrangements.

3. Consider the letters in the word COMPUTER. In how many different ways can the letters
be arranged
a) In such a way that vowels may occupy only odd positions?
b) If the vowels are to be separated from each other?
c) If the consonants are to be together?

4. From digits 0, 1, 2, 3, 4, how many arrangement are there for those five digits numbers
can be made:
a) If repetition is allowed
b) If repetition is not allowed
c) Between 10,000 and 30,000 with no repetition

5. Three-digit numbers are to be formed from the digits 0, 2, 3, 4 and 8 (excluding number
which begins with 0). How many numbers can be formed when
a) repetition is allowed.
b) repetition is not allowed.

6. How many 4 digit numbers can be formed using 4 different digits from 1, 2, 3, 4, 5, 6?
How many of these numbers are odd and greater than 5000?

BKS 2019/20 Page 1

7. A 4-digit numberis formed from 3, 4, 5, 6 and 7.
(a) How many different ways can 4-digit number be formed?
(b) How many different ways can 4-digit numbers is divisible by 5?
(c) How many different 4_digit numbers is less than 5000?

8 . A four-digit number is to be formed from the digits 0,1,2,3,4,5,6,7,8 and 9 without
repetition. How many
(a) four-digit numbers between 3000 and 7000 can be formed?
(b) four-digit even numbers less than 6000 can be formed?

BKS 2019/20 Page 2

Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia
JOM-DO-MATHS (JDM)
Chapter 7 Permutations and Combinations( Set 2 )
1. Find the number of ways of choosing at least 4 students from 6 students to
represent their class in a drawing contest.

2. The Mathematics paper in a test has two sections, A and B. Section A has 10
questions and section B has 8 questions. A candidate can answer either 5
questions from section A and 4 questions from section B or 4 questions from
section A and 5 questions from section B. Find the number of different
combination of questions a candidate can answer.

3. Gift packs consisting of 6 items each are to be prepared for children’s day
celebration. If the items are chosen from 4 different pencil cases and 5
different boxes of watercolours, calculate the number of ways the gift packs
can be prepared if each one must consist of not more than 3 boxes of
watercolours.

4. A dancing team comprising of 6 person are to be selected from 20 children, 10
men and 8 women. Find the number of ways the team can be formed if
(a) The team must consist of 3 children, 2 men and a woman.
(b) There are equal number of children, men and women.

5. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2
vowels can be formed ?

6. In a group of 6 boys and 4 girls, four children are to be selected. In how many
different ways can they be selected such that at least one boy should be there?

BKS 2019/20 IMS

7 From a group of 7 men and 6 women, five persons are to be selected to form
a committee so that at least 3 men are there in the committee. In how many
ways can it be done?

8. A committee of 8 members consists of husband and wife together with four
other men and two other women. From the committee, a social worker group
of four persons is to be formed
(a) Find the number of different social workers can be formed
(b) In how many ways can the group of social workers be formed if
i. It may not contain both husband and wife
ii. It must contain two men and two women
iii. It must contain at least one men and at least one women

9. Twelve cards of similar color and size are labeled each with a number from 1
to 12. In how many ways can
a) 7 cards be selected such that 4 cards are labeled with even numbers and
remaining cards are labeled with odd numbers?

b) 9 cards be arranged in a row such that the first 5 cards are labeled with even
numbers and the remaining cards are labeled with odd numbers?

c) 9 cards be arranged in a row such that 5 cards are labeled with even numbers
and the remaining cards are labeled with odd numbers?

10. (a) A box contains 5 identical white marbles and 4 identical black marble . 4
marbles are taken from the box and arranged in a row. How many ways
can the marbles be arranged ?
(b) 14 empty bottles of similar shape and size are labelled with a number from
1 to 14 . In how many ways can
(i) 7 bottles be selected such that 4 are labelled with odd numbers and the
rest with even numbers?
(ii) 5 bottles be arranged in a row such that the first 3 bottles are
labelled with odd numbers and the other 2 with even numbers?

BKS 2019/20 IMS

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