Probability Question 23
Question: 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
[Kurukshetra CEE 1996; DCE 1999]
Options:
A) $ \frac{10}{21} $
B) $ \frac{8}{63} $
C) $ \frac{5}{21} $
D) $ \frac{9}{21} $
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Answer:
Correct Answer: A
Solution:
Total number of ways $ ={}^{9}C_4, $ 2 children are chosen in $ {}^{4}C_2 $ ways and other 2 persons are chosen in $ {}^{5}C_2 $ ways.
Hence required probability = $ \frac{{}^{4}C_2\times {}^{5}C_2}{{}^{9}C_4}=\frac{10}{21}. $
BETA
