Solved: A school committee of 5 is to be formed from 7 male…

Here are the solutions to the questions:

6. (ii) A school committee of 5 is to be formed from 7 male teachers, 6 female teachers, and the principal.

a) In how many ways can the committee be formed if it must include exactly 3 male teachers and 2 female teachers?

Choose 3 male teachers from 7.
Number of ways = $\binom{7}{3} = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$ .
Choose 2 female teachers from 6.
Number of ways = $\binom{6}{2} =

A school committee of 5 is to be formed from 7 male teachers, 6 female teachers, and the principal. In how many ways can the committee be formed if it must include exactly 3 male teachers and 2 female