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27 May, 00:53

A business organization needs to make up a 7 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at least 4 accounting majors are on the committee?

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  1. 27 May, 01:19
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    Answer: 658 ways.

    Step-by-step explanation:

    To find the number of ways the number "r" items can be chosen from the available number "n", the combination formula for selection is used. This formula is denoted as:

    nCr = n! / (n-r) ! * r!

    Where n! = n * (n-1) * (n-2) ... * 3*2*1.

    If we have 6 accounting majors and 7 finance majors and we are to choose a 7-member committee from these with at least 4 accounting majors on the committee, then the possibilities we have include:

    [4 accounting majors and 3 finance majors] Or [5 accounting majors and 2 finance majors] or [ 6 accounting majors and 1 finance major].

    Mathematically, this becomes:

    [6C4 * 7C3] + [6C5 * 7C2] + [6C6*7C1]

    525 + 126 + 7 = 658 ways.

    Note: it is 6C4 because we are choosing 4 accounting majors from possible 6. This applies to other selection possibilities.
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