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Math Help - Number of combinations

  1. #1
    Member Jones's Avatar
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    Number of combinations

    Hi,

    I have this problem that i can't get right.

    A team of 5 people are selected to participate in a chess tournament.
    The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.

    In how many ways can the team be selected?

    So i thought this would be as simple as:

    Either 2 boys and 3 girls or 3 boys and 2 girls.

    [Math](17*16*15/3) * (13*12/2)*(13*12*11/3)*(17*16/2)[/tex]

    That is incorrect though...

    Any ideas on how to do this?
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  2. #2
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    Quote Originally Posted by Jones View Post
    Hi,

    I have this problem that i can't get right.

    A team of 5 people are selected to participate in a chess tournament.
    The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.

    In how many ways can the team be selected?

    So i thought this would be as simple as:

    Either 2 boys and 3 girls or 3 boys and 2 girls.

    (17*16*15/3) * (13*12/2)*(13*12*11/3)*(17*16/2)

    That is incorrect though...

    Any ideas on how to do this?
    2 boys and 3 girls:  {17 \choose 2} \cdot {13 \choose 3} = \, ....

    3 boys and 2 girls:  {17 \choose 3} \cdot {13 \choose 2} = \, ....

    Now add the two numbers together.
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  3. #3
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    Quote Originally Posted by Jones View Post
    A team of 5 people are selected to participate in a chess tournament. The "team" is picked within a school class with 17 boys and 13 girls. The rules state that the team must consist of at least 2 boys and 2 girls.
    {{17}\choose{3}}{{13}\choose{2}}+{{17}\choose{2}}{  {13}\choose{3}}.
    That choose three boys and two girls or two boys and three girls.
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  4. #4
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    Quote Originally Posted by Plato View Post
    {{17}\choose{3}}{{13}\choose{2}}+{{17}\choose{2}}{  {13}\choose{3}}.
    That choose three boys and two girls or two boys and three girls.
    A rare event - we both get the same answer (which means I've got a combinatorial question correct for once).
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  5. #5
    Member Jones's Avatar
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    hah, it turned out to be really easy.

    Did i make a twat out of myself?
    Last edited by Jones; October 22nd 2008 at 11:07 AM.
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