In how many ways can committee of 5 be made out of 6 men and 4 women, containing at least 2 women?

We need to include at least 2 women. If we include 2 women in the committee, then a number of men is 3. The number of ways, 2 women can be selected out of 4 is = 4C2 = 6 The number of ways, 3 men can be selected out of 6 is = 6C3 = 20 So, the committee can be formed including 2 women in (20 X 6) = 120 ways. If we include 3 women in the committee, then a number of men is 2. The number of ways, 3 women can be selected out of 4 is = 4C3 = 4 The number of ways, 2 men can be selected out of 6 is = 6C2 = 15 So, the committee can be formed including 3 women in (15 X 4) = 60 ways. Therefore, the total number of ways the committee can be formed is = (120 + 60) = 180 ways.


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