NDA 2025 · PYQ · Probability / Combinations · medium
A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee includes exactly 3 gentlemen?
A.10/33✓ Correct
B.30/77
C.100/231
D.5/11
Explanation
Total ways to form committee of 6 from 11 = C(11,6) = 462. Ways with exactly 3 gentlemen and 3 ladies = C(7,3)·C(4,3) = 35·4 = 140. Probability = 140/462 = 10/33.
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