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Question
Form a group of 4 men, 4 women and 3 children, 4 persons are selected at random. Find the probability that, no child is selected.
Solution
The group consists of 4 men, 4 women and 3 children, i.e., 4 + 4 + 3 = 11 persons.
4 persons are to be selected from this group.
∴ 4 persons can be selected from 11 persons in 11C4 ways.
∴ n(S) = 11C4
Let event A: No child is selected.
∴ 4 persons can be selected from 4 men and 4 women, i.e., from 8 persons in 8C4 ways.
∴ n(A) = 8C4
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(""^8"C"_4)/(""^11"C"_4)`
= `(8 xx 7 xx 6 xx 5)/(11 xx 10 xx 9 xx 8)`
= `1680/7920`
= `7/33`
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