Question
A committee of 4 members is to be formed from 6 men and
4 women. Find the probability that the committee will have at least 2 women.Solution
ATQ,
Total number of ways to form a committee of 4 from 10 people: = 10C4 = 210. Now, favorable cases (at least 2 women): Possible cases: (2W, 2M), (3W, 1M), (4W, 0M) Case 1: 2W, 2M = 4C2 × 6C2 = 6 × 15 = 90 Case 2: 3W, 1M = 4C3 × 6C1 = 4 × 6 = 24 Case 3: 4W, 0M = 4C4 × 6C0 = 1 × 1 = 1 Total favorable = 90 + 24 + 1 = 115 Probability = favorable / total = 115 / 210 = 23 / 42
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