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Math Help - select a committie with brother and sister

  1. #1
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    select a committie with brother and sister

    Hi,

    Not sure about this answer.

    A sub committee of 3 women and 2 men is to be chosen at random from a committee of 5 women and 7 men. In the original committee are a brother and sister. Find the probability that both the brother and sister are both selected to work on the sub committee

    cheers
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  2. #2
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    Quote Originally Posted by Joel View Post
    Hi,

    Not sure about this answer.

    A sub committee of 3 women and 2 men is to be chosen at random from a committee of 5 women and 7 men. In the original committee are a brother and sister. Find the probability that both the brother and sister are both selected to work on the sub committee

    cheers
    I would say that for the numerator you would have C(5,1)*C(7,1) for the selection of the brother and sister.

    For the denominator the total possibilities would be C(5,3)*C(7,2).

    Result: .167
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  3. #3
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    Quote Originally Posted by mikeyS View Post
    I would say that for the numerator you would have C(5,1)*C(7,1) for the selection of the brother and sister.
    For the denominator the total possibilities would be C(5,3)*C(7,2).
    You have the denominator correct, but not the numerator.
    Try \binom{4}{2}\binom{6}{1}. WHY?
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  4. #4
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    Quote Originally Posted by Plato View Post
    You have the denominator correct, but not the numerator.
    Try \binom{4}{2}\binom{6}{1}. WHY?

    I guess I tried this one before my second cup o' joe.

    Looking at the sub-committee we will have groups like:
    sister, not sister, not sister and brother, not brother

    So we place the sister and brother leaving 4 and 6 members left to fill 2 and 1 spot(s), respectively. Thus to fill the remainder we have C(4,2) and C(6,1)
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