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A committee of 3 people is to be chosen at random from a group of 5 women and 4 men. What is the probability that the committee includes at least one woman and at least one man?
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Correct answer
B
At least one of each is the complement of the two bad cases: an all-women committee or an all-men committee. Total committees are C(9,3) = 84.
All-women committees number C(5,3) = 10 and all-men committees number C(4,3) = 4, so the bad cases total 10 + 4 = 14. Thus the favorable probability is 1 − 14/84 = 70/84 = 5/6, choice (B).
The two near-miss wrong answers are (C) 37/42, which removes only the all-women case, and (D) 20/21, which removes only the all-men case.
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