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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