CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
116
PAPER 1
1. A committee of 3 boys and 3 girls are to be formed from 10 boys and 11 girls.
In how many ways can the committee be formed?
[2 marks]
2. How many 4-letter codes can be formed using the letters in the word 'GRACIOUS' without
repetition such that the first letter is a vowel?
[2 marks]
3. Find the number of ways of choosing 6 letters including the letter G from the word
'GRACIOUS'.
[2 marks]
4. How many 3-digit numbers that are greater than 400 can be formed using the digits 1, 2, 3, 4,
and 5 without repetition?
[2 marks]
5. How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, and 5 without
repetition?
[2 marks]
6. Diagram shows 4 letters and 4 digits.
A code is to be formed using those letters and digits. The code must consists of 3 letters
followed by 2 digits. How many codes can be formed if no letter or digit is repeated in each
code ?
[3 marks]
7. A badminton team consists of 8 students. The team will be chosen from a group of 8 boys and
5 girls. Find the number of teams that can be formed such that each team consists of
a) 5 boys,
b) not more than 2 girls.
[4 marks]
8. Diagram shows five cards of different letters.
a) Find the number of possible arrangements, in a row, of all the cards.
b) Find the number of these arrangements in which the letters A and N are side by side.
[4 marks]
A B C D 5 6 7 8
R A J I N
CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
117
9. A debating team consists of 6 students. These 6 students are chosen from 2 monitors, 3
assistant monitors and 5 prefects.
a) there is no restriction,
b) the team contains only 1 monitor and exactly 3 prefects.
[4 marks]
10. Diagram shows seven letter cards.
A five-letter code is to be formed using five of these cards. Find
a) the number of different five-letter codes that can be formed,
b) the number of different five-letter codes which end with a consonant.
[4 marks]
11. How many 5-digit numbers that are greater than 50000 can be formed using the digits 1, 2, 3, 4,
5, 6, 7, 8, and 9 without repetition?
[4 marks]
12. How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 without any
digit being repeated?
[4 marks]
13. A coach wants to choose 9 players consisting of 6 boys and 3 girls to form a squash team.
These 9 players are chosen from a group of 8 boys and 6 girls. Find
(a) the number of ways the team can be formed,
(b) the number of ways the team members can be arranged in a row for a group photograph,
if the 6 boys sit next to each other. [4 marks]
14. 2 girls and 8 boys are to be seated in a row of 5 chairs. Find the number of ways they can be
seated if no two persons of the same sex are next to each other.
[3 marks]
15. Diagram shows six numbered cards.
A four-digit number is to be formed by using four of these cards.
How many
a) different numbers can be formed?
b) different odd numbers can be formed?
[4 marks]
R O F I N U M
9 8 7 5 4 1
CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
118
ANSWERS ( PAPER 1 )
1. 3
10C x 3
11C 1
= 19800
1
2. 1
4 p x 3
7 p 1
= 840
1
3. 1 x 5
7C 1
= 21
1
4. 1
2 p x 2
4 p 1
= 24
1
5. 3
4 p x 1
2 p 1
= 48
1
6. 3
4 p x 2
4 p 2
= 288
1
7. a) 5
8C x 3
5C = 560 1
b) If the team consists of 8 boys and 0 girl 8
8C x 0
5C = 1
If the team consists of 7 boys and 1 girl 7
8C x 1
5C = 40
If the team consists of 6 boys and 2 girl 6
8C x 2
5C = 280
1
The number of teams that can be formed = 1 + 40 + 280 1
= 321
1
8. a) 5! = 120 1
b) 4! x 2! 2
= 48
1
9. a) 6
10C = 210 2
b) 1
2C x 3
5C x 2
3C = 60 2
10. a) 5
7 p = 2520 2
b) 4
6 p x 1
4 p 1
= 1440
1
11. 1
5 p x 4
8 p 2
= 8400
1
12. 3
5 p x 1
3 p = 180 2
= 180
1
CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
119
13. a) 6
8C 3
6C 1
= 560 1
b) 6! x 4! 1
= 17280 1
14. 3
8 P x 2
2 P 2
= 672 1
15. a) 6P4 = 360
1
b) 5P3 x
4P1 2
= 240 1
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