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16 December, 01:30

There are nine men and ten women in a club; in how many ways can a committee of four be formed to include at least 1 man?

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  1. 16 December, 05:03
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    The number of combinations of the 19 people taken 4 at a time is:

    19C4 = 3876.

    The number of combinations with no men is:

    10C4 = 210.

    Therefore the number of ways of forming a committee of four including at least one man is:

    3876 - 210 = 3666.

    The answer is 3666 ways.
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