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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, exactly 2 men are selected
Solution
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`
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