A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

Men = 2

Women = 3

A committee of 3 persons to be constituted.

Here, the order does not matter.

Therefore, we need to count combinations.

There will be as many committees as combinations of 5 different persons taken 3 at a time.

Hence, the required number of ways = ⁵C₃

= 5!/(3! 2!)

= (5 × 4 × 3!)/(3! × 2)

= 10

Committees with 1 man and 2 women:

1 man can be selected from 2 men in ²C₁ ways.

2 women can be selected from 3 women in ³C₂ ways.

Therefore, the required number of committees = ²C₁ × ³C₂

= 2 × ³C₁

= 2 × 3

= 6