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 - Mathematics

MCQ

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

Options

11/21
9/21
10/21
none of these

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Solution

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 = \[\frac{60}{126} = \frac{10}{21}\]