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You can have

4 women and 1 man in C(10,4) x C(15,1) = 3150 ways

3 " 2 " in C(10,3) x C(15,2) = 12600 "

2 " 3 " in C(10,2) x C(15,3) = 20475 "

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Total = 36225 <---------

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Q: How many different 5 persons committees can be formed each containing at least 2 women and at least one man from a set of 10 women and 15 men?
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