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Question: If four persons are chosen at random from a group of 3 men, 2 women and 4 children. Then the probabi...

If four persons are chosen at random from a group of 3 men, 2 women and 4 children. Then the probability that exactly two of them are children is

A

10/21

B

8/63

C

5/21

D

9/21

Answer

10/21

Explanation

Solution

Total number of ways = 9C4, 6mu29C_{4},\mspace{6mu} 2 children are chosen in 4C24C_{2} ways and other 2 persons are chosen in 5C25C_{2} ways.

Hence required probability = 4C2x5C29C4=1021\frac{4C_{2}x^{5}C_{2}}{9C_{4}} = \frac{10}{21}