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1. From 6 boys and 4 girls, 5 are to be selected for admission for a particular course. In how many ways can this be done if there must be exactly 2 girls?
- A. 60
- B. 60
- C. 60
- D. 60
Answer: Option D
Explanation:
nCr = combination of n things taken r at a time = n!/((n - r)!*r!)
Number of ways to select 2 girls (exactly) from 4 - 4C2
6C3 - Number of ways to select remaining 3 boys from 6 to make total 3 + 2 = 5 for admission.
6C3 = 6!/(3!*3!) = 720/(6*6) = 20
4C2 = 4!/(2!*2!) = 24/4 = 6.
So, 6C3*4C2 = 20*6 = 120 ways.
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