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Math Help - combinatorics

  1. #1
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    combinatorics

    A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?

    Please show formulas.

    Thanks,
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  2. #2
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    Quote Originally Posted by gogo08
    A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?

    Please show formulas.

    Thanks,
    Possibilities
    0 Girls
    1 Girl
    2 Girls

    In each case respectively we have,
    _{10}C_4 \cdot _{12}C_0=210
    _{10}C_3 \cdot _{12}C_1=1440
    _{10}C_2 \cdot _{12}C_2=2970
    In total,
    4260
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