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 this committee would consist of 1 man and 2 women?

Question

Philoid · Accepted Answer

Given that we need to select 3 persons out of 2 men and 3 women,

Let us assume the no. of ways of selecting be N,

⇒ N = selecting 3 persons out of total 5 persons

⇒ N = ⁵C₃

We know that

And also n! = (n)(n – 1)(n – 2)…………2.1

⇒

⇒ N = 10 ways

The no. of ways of selecting 3 persons out of 2 men and 3 women is 10.

(ii) It is told that 1 man and 2 women should be selected out of 2 men and 3 women.

Let us assume the no. of ways of selection be N₁,

⇒ N₁ = (selecting one man out of 2 men) × (selecting 2 women out of 3 women)

⇒ N₁ = (²C₁) × (³C₂)

We know that

And also n! = (n)(n – 1)(n – 2)…………2.1

⇒

⇒ N₁ = 6 ways

The no. of ways of selecting 1 man and 2 women is 6.