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Question: Answered & Verified by Expert
A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?
MathematicsProbabilityNDANDA 2018 (Phase 1)
Options:
  • A $\frac{5}{14}$
  • B $\frac{1}{21}$
  • C $\frac{3}{14}$
  • D $\frac{8}{21}$
Solution:
1378 Upvotes Verified Answer
The correct answer is: $\frac{5}{14}$
$\mathrm{n}(\mathrm{E})={ }^{4} \mathrm{C}_{2} \times{ }^{5} \mathrm{C}_{1}=6 \times 5=30$.
$\mathrm{n}(\mathrm{S})={ }^{9} \mathrm{C}_{3}=84$
$\therefore$ Probability, $\mathrm{P}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{30}{84}=\frac{5}{14}$

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