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.

Answer 1

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)`