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In how many ways can a committee of 7 people be chosen from 15 married couples if 2 couples must be on the committee?

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There are 15C2 ways to choose the couples. That uses up 4 people, leaving 26 individuals to make up the other 3 places on the committee. So, you have

15C2 * 26C3 = 105 * 2600 = 273,000 ways

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