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Math 117

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

  • Math 117 -

    With no girls
    C(10,4) = 210 ways
    With one girl
    12 C(10,3) = 12*120 = 1440 ways
    With two girls
    first combinations of 12 girls taken 2 at a time = 12!/[10!*2!) = 12*11/2 = 66
    (my table of binomial coefficients only goes to n = 10)
    time combinations of ten boys taken 2 at a time = C(10,2) = 45
    so 66*45 = 2970
    so
    2970+1440+210

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