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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
Options
11/21
9/21
10/21
none of these
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 = \[\frac{60}{126} = \frac{10}{21}\]
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