SOLUTION: There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be selected if there must be 2 men and 2 women?

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Question 1051110: There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be selected if there must be 2 men and 2 women? How many ways can this committee be selected if there must be at least 2 women on the committee?
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Answer by stanbon(75887) About Me  (Show Source):
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Probability-and-statistics/1051110 (2016-10-03 17:42:57): There are 7 women and 5 men in a department.
How many ways can a committee of 4 people be selected?
Ans: 12C4 = (12*11*10*9)/(1*2*3*4) = 495
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How many ways can this committee be selected if there must be 2 men and 2 women?
Ans: 7C2*5C2 = 21*10 = 210
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How many ways can this committee be selected if there must be at least 2 women on the committee?
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2 women + 3 women + 4 women
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7C2*5C2 + 7C3*5C1 + 7C4 = 21*10 + 35*5 + 35 = 210 + 175 + 35 = 420 ways
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Cheers,
Stan H.
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