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Question

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is
(a) 11/21
(b) 9/21
(c) 10/21
(d) none of these

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Solution

(c) 10/21

There are nine persons (three men, two women and four children) out of which four persons can be selected in 9C4 = 126 ways.
∴ Total number of elementary events = 126
Exactly two children means selecting two children and two other people from three men and two women.
This can be done in 4C2 × 5C2 ways.
∴ Favourable number of elementary events = 4C2 × 5C2 = 60
So, required probability = 60126=1021

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