Question

Form a group of 4 men, 4 women and 3 children, 4 persons are selected at random. Find the probability that, exactly 2 men are selected

Answer 1

Total number of persons = 4 + 4 + 3 = 11

Four persons can be selected from these 11 persons in ¹¹C₄ ways.

∴ n(S) = ¹¹C₄

= `(11*10*9*8)/(1*2*3*4)`

= 11 × 10 × 3

Let B ≡ the event that exactly 2 men are selected Since 2 men are to be selected,

we have to select 2 men out of 4 men and 2 persons from the remaining 7 persons which can be done in ⁴C₂ × ⁷C₂ ways.

∴ n(B) = ⁴C₂ × ⁷C₂

= `(4*3)/(1*2) xx (7*6)/(1*2)`

= 2 × 3 × 7 × 3

∴ the required probability = P(B)

= `("n"("B"))/("n"("S"))`

= `(2 xx 3 xx 7 xx 3)/(11 xx 10 xx 3)`

= `21/55`