Q. 30 C5.0( 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 :

at most 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.


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


The possible cases are the following:


i. Selecting 3 girls and 4 boys


ii. Selecting 2 girls and 5 boys


iii. Selecting 1 girl and 6 boys


iv. Selecting 7 boys


Let us assume the no. of ways of selecting is N2.


N2 = ((no. of ways of selecting 3 girls out of 4 girls) × (no. of ways of selecting 4 boys out of 9 boys)) × ((no. of ways of selecting 2 girls out of 4 girls) × (no. of ways of selecting 5 boys out of 9 boys)) × ((no. of ways of selecting 1 girls out of 4 girls) × (no. of ways of selecting 6 boys out of 9 boys))


N2 = ((4C3) × (9C4)) + ((4C2) × (9C5)) + ((4C1) × (9C6)) + (9C7)


We know that ,


And also n! = (n)(n – 1)......2.1





N2 = (4 × 126) + (6 × 126) + (4 × 84) + (36)


N2 = 504 + 756 + 336 + 36


N2 = 1632


The no. of ways of selecting 7 members with at most 3 girls is 1632.


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