Q. 30 A5.0( 1 Vote )

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 :

exactly 3 girls?

Answer :

Given that we need to select 7 members out of 9 boys and 4 girls by following the conditions:


i. exactly 3 girls


ii. at least 3 girls


iii. at most 3 girls.


i. It is told we need to select 7 members out of 9 boys and 4 girls with exactly 3 girls.


Let us assume the no. of ways of selecting is N.


N = (no. of ways of selecting 3 girls out of 4 girls) × (no. of ways of selecting 4 boys out of 9 boys)


N = (4C3) × (9C4)


We know that ,


And also n! = (n)(n – 1)......2.1





N = 4 × 126


N = 504


The no. of ways of selecting 7 members with exactly 3 girls is 504.


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