Permutation Short Questions (Question 5 - 8)


Question 5:
A committee that consists of 6 members is to be selected from 5 teachers and 4 students. Find the number of different committees that can be formed if
(a) there is no restriction,
(b) the number of teachers must exceed the number of students.

Solution:
(a)
Total number of committees = 5 + 4 = 9
6 members to be selected from 9 committees with no restriction
= 9 C 6 =84

(b)
If the number of teachers must exceed the number of students, the combination = 4 teachers 2 students + 5 teachers 1 student =   5 C 4 ×   4 C 2 +   5 C 5 ×   4 C 1 =30+4 =34


Question 6:
Six members of a committee of a school are to be selected from 6 male teachers, 4 female teachers and a male principal. Find the number of different committees that can be formed if
(a) the principal is the chairman of the committee,
(b) there are exactly 2 females in the committee,
(c) there are not more than 4 males in the committee.

Solution:
(a)
If the principal is the chairman of the committee, the remaining number of committee is 5 members.
Hence, the number of different committees that can be formed from the remaining 6 male teachers and 4 female teachers
=   10 C 5 =252

(b)
Exactly 2 females in the committee 4 C 2 ×   7 C 4 =210

(c)
There are not more than 4 males in the committee = 4 males 2 females + 3 males 3 females + 2 males 4 females  =   7 C 4 ×   4 C 2 +   7 C 3 ×   4 C 3 +   7 C 2 ×   4 C 4 =210+140+21 =371



Question 7:
A school prefect committee that consists of 6 persons is to be chosen from 6 Malays, 5 Chinese and 4 Indians. Calculate the number of different committees that can be formed if the number of Malays, Chinese and Indians must be equal.

Solution:
Number of different committees that can be formed for 2 Malays, 2 Chinese and 2 Indians
=   6 C 2 ×   5 C 2  ×   4 C 2 =900


Question 8:
There are 10 different flavour candies in a plastic bag.
Find
(a) the number of ways 3 candies can be chosen from the plastic bag.
(b) the number of ways at least 8 candies can be chosen from the plastic bag.

Solution:
(a)
Number of ways choosing 3 candies out of 10 candies
=   10 C 3 =120

(b)
Number of ways choosing 8 candies =   10 C 8
Number of ways choosing 9 candies = 10 C 9
Number of ways choosing 10 candies = 10 C 10

Hence, number of ways of choosing at least 8 candies
=   10 C 8 10 C 9 +   10 C 10 =56