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Question
From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains 3 boys and 2 girls.
Solution
The group consists of 8 boys and 5 girls
i.e., 8 + 5 = 13 persons.
A committee of 5 is to be formed from this group.
∴ 5 persons from 13 persons can be selected in 13C5 ways
∴ n(S) = 13C5
Let A be the event that the committee contains 3 boys and 2 girls.
3 boys from 8 boys can be selected in 8C3 ways and 2 girls from 5 girls can be selected in 5C2 ways
∴ n(A) = 8C3 × 5C2
∴ P(A) = `("n"("A"))/("n"("S")`
= `(""^8"C"_3 xx ""^5"C"_2)/(""^13"C"_5)`
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