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.

Answer 1

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`