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9 October, 15:15

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3 person committee be created if the committee must include the male employee?

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  1. 9 October, 17:46
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    We can approach this as how many 2 person female committees can we make that we can add the male to.

    5 C 2 (combinations of 5 taken 2 at a time order doesn't matter)

    5 x 4 = 20 = 10 ways. Since the male can join any of the groups there are

    2 x 1 2 still 10 ways.

    Here's another way of looking at it. Let's call the five females A, B, C, D and E

    Here are the pairings:

    AB BC CD DE

    AC BD CE

    AD BE

    AE The male can be the 3rd person in any group. Once

    again, there are 10 ways to do this.
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