Q. 205.0( 1 Vote )

# 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?

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 = ^{5}C_{3}

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 N_{1},

⇒ N_{1} = (selecting one man out of 2 men) × (selecting 2 women out of 3 women)

⇒ N_{1} = (^{2}C_{1}) × (^{3}C_{2})

We know that

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

⇒

⇒

⇒

⇒ N_{1} = 6 ways

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

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