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Math Help - Number of ways to get a 10-person committee

  1. #1
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    Number of ways to get a 10-person committee

    How many ways are there to form a 10-person committee from 13 women and 18 men so that there is at least one woman on the committee?


    Okay, I think I know what to do with this, but I want to be sure I going about it the right way. I will use (n)C(k) as notation for "n choose k".

    First, the number of total committees regardless of gender would be (31)C(10). Then I just subtract the number of ways to get a committee of all men, which would be (18)C(10). So my final answer would be (31)C(10) - (18)C(10). Is this correct?
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  2. #2
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    Yes that is correct.
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