CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
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 B C D 5 6 7 8
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.
R A J I N
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]
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CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
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.
U N I F O R M
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.
1 4 5 7 8 9
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?
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CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
[4 marks]
ANSWERS ( PAPER 1 )
1. 10
C3 x 11
C3 1
= 19800 1
2. 4
p1 x 7
p3 1
= 840 1
3. 1 x C5
7
1
= 21 1
4. 2
p1 x 4
p2 1
= 24 1
5. 4
p3 x 2
p1 1
= 48 1
6. 4
p3 x 4
p2 2
= 288 1
7. a)
8
C 5 x 5 C 3 = 560 1
8 5
b) If the team consists of 8 boys and 0 girl C8 x C 0 =1
If the team consists of 7 boys and 1 girl
8 5
C 7 x C1 = 40 1
8
If the team consists of 6 boys and 2 girl C 6 x 5 C 2 = 280
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)
10
C 6 = 210 2
b) 2
C1 x 5 C 3 x 3
C 2 = 60 2
10. a)
7
p 5 = 2520 2
6
b) p 4 x 4 p1 1
= 1440
1
11. 5
p1 x 8 p 4 2
= 8400
1
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CHAPTER 6 PERMUTATIONS AND COMBINATIONS FORM 5
12. 5
p3 x 3
p1 = 180 2
= 180
1
13. a)
8
C6 6
C3 1
= 560 1
b) 6! x 4! 1
= 17280 1
14. 8
P3 x 2
P2 2
= 672 1
6
15. a) P4 = 360 1
5
b) P3 x 4P1 2
= 240 1
119
