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Math Help - Discrete Mathamatics

  1. #1
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    Discrete Mathamatics

    A committee of 7 people is to be formed form a group of 20 people, 11 of which are women?

    a) In how many ways can this be done?

    b)If the committee must consist of 4 women and 3 men, in how many ways can this be done?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by msmall13@yahoo.com View Post
    A committee of 7 people is to be formed form a group of 20 people, 11 of which are women?

    a) In how many ways can this be done?
    The number of ways this can be done is \binom{20}7=\frac{20!}{7!13!}. We use combinations, for order doesn't matter here.

    b)If the committee must consist of 4 women and 3 men, in how many ways can this be done?
    The number of ways this can be done is \binom{11}4\binom93\binom{20}7 (I believe...can someone verify this?)

    Do you see why this is the case?

    I hope this helps!

    --Chris
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  3. #3
    Moo
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    Hello,
    Quote Originally Posted by Chris L T521 View Post
    The number of ways this can be done is \binom{11}4\binom93{\color{red}\binom{20}7} (I believe...can someone verify this?)

    Do you see why this is the case?

    I hope this helps!

    --Chris
    Why is there the red part ?
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