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4 February, 18:35

A business organization needs to make up a 5 member fund-raising committee. The organization has 10 accounting majors and 8 finance majors. In how many ways can the fund-raising committee be formed if at most 2 accounting majors are on the committee?

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  1. 4 February, 18:55
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    The fund raising committee can be organized in 3,276 different ways.

    Explanation:

    The committee can have the following structures:

    Accounting majors Finance majors

    0 5

    1 4

    2 3

    C (10,0) x C (8,5) = (10! / 10!) x (8! / 3!5!) = 1 x 56 = 56

    C (10,1) x C (8,4) = (10! / 9!1!) x (8! / 4!4!) = 10 x 70 = 700

    C (10,2) x C (8,3) = (10! / 8!2!) x (8! / 5!3!) = 45 x 56 = 2,520

    total possibilities = 2,520 + 700 + 56 = 3,276
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