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Math Help - Combinations of"" problem

  1. #1
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    Combinations of"" problem

    How many committed of size 15, from a group of 20 men and 30 women, contain both genders?


    what I find difficult is the difference of numbers within the gender where if it were just 50 people taken 15 at a time id have no problem.


    thanks
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  2. #2
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    Re: Combinations of"" problem

    Quote Originally Posted by lhurlbert View Post
    How many committed of size 15, from a group of 20 men and 30 women, contain both genders?
    There is a total of \binom{50}{15} possible committees

    Of those \binom{20}{15} are all male and \binom{30}{15} are all female.

    Subtract those off. The committees left are mixed genders.
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  3. #3
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    Re: Combinations of"" problem

    And that's combination? I haven't seen that notation () yet
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  4. #4
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    Re: Combinations of"" problem

    Hello, lhurlbert!

    And that's combination?
    I haven't seen that notation () yet.

    Yes, that is an alternative symbol for combinations.

    . . {50\choose15} \;=\;_{50}C_{15} \;=\;\frac{50!}{15!\,35!}
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