A committee

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.