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  1. #1
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    Math Riddle- Help

    A company personnel director must hire 6 people: 4 for the assembly department and 2 for the shipping department. There are 10 applicants who are equally qualified to work in each department. In how many ways can the personnel director fill the position?
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  2. #2
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    Hello, kensington!

    A company personnel director must hire 6 people:
    . . 4 for the assembly department and 2 for the shipping department.

    There are 10 applicants who are equally qualified to work in each department.

    In how many ways can the personnel director fill the position?

    We will partition the 10 applicants into 3 groups:
    . . 4 for the aseembly department,
    . . 2 for the shipping department,
    . . 4 who are not hired.

    The number of partitions is: . \displaystyle{10\choose4,2,4} \;=\;\frac{10!}{4!\,2!\,4!} \;=\;3150

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