A committee of 4 people is to be selected from a group of 6 men and 5 women. What is the probability that the committee contains exactly 2 men and 2 women?
Answer and explanation
Correct answer: D. 5/11
- Step 1: Total ways to choose 4 people from 11: C(11, 4) = (11 10 9 8) / (4 3 2 1) = 330.
- Step 2: Ways to choose 2 men from 6: C(6, 2) = (6 * 5) / 2 = 15.
- Step 3: Ways to choose 2 women from 5: C(5, 2) = (5 * 4) / 2 = 10.
- Step 4: Favorable outcomes = 15 * 10 = 150.
- Step 5: Probability = 150 / 330 = 15 / 33 = 5 / 11.
Answer
5/11.
Why not the others: 3/11 computes 90/330; 6/11 computes 180/330; 1/2 is an unweighted estimate.
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