Question

Out of 6 teachers and four boys, a committee of eight is to be formed. In how many ways
can this be done when there should not be less than four teachers in the committee.
(a) 45
(b) 55
(c) 30
(d) 50​

Answer 1

Given:

Total number of teachers = 6

Total number of boys = 4

Number of members needed to form the committee = 8

To find:

In how many ways a committee can be formed with not less than 4 teachers in the committee.

Solution:

Since there should not be less than 4 teachers, the possibilities to form a committee are:

4 teachers 4 boys = 6C4 * 4C4 = 15

5 teachers 3 boys = 6C5 * 4C3 = 24

6 teachers 2 boys = 6C6 * 4C2 = 6

Total possibility = 15 + 24 + 6 = 45

Therefore, there are 45 ways in which a committee of 8 members can be formed with at least 4 teachers in it.