#### Question

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?

#### Solution

A committee of 7 has to be formed from 9 boys and 4 girls.

i) Since exactly 3 girls are to be there in every committee, each committee must consist of (7 – 3) = 4 boys only.

(ii) Since at least 3 girls are to be there in every committee, the committee can consist of

(a) 3 girls and 4 boys or (b) 4 girls and 3 boys

3 girls and 4 boys can be selected in `""^4C_3 xx ""^9C_4` ways.

4 girls and 3 boys can be selected in `""^4C_4 xx ""^9C_3` ways.

(iii) Since atmost 3 girls are to be there in every committee, the committee can consist of

(a) 3 girls and 4 boys (b) 2 girls and 5 boys

(c) 1 girl and 6 boys (d) No girl and 7 boys