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23 February, 21:42

The senate in a certain state is compromised of 58 republicans, 39 democrats, and 3 independents. How many committees can be formed if each committee must have 3Republicans and 2 Democrats?

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  1. 23 February, 22:03
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    Defining C (n, r) as the number of combinations (order does not count) to choose r objects from n, where C (n, r) = n! / (r! (n-r) !)

    there are

    C (58,3) ways to choose 3 from 58 republicans,

    and

    C (39,2) ways to choose 2 from 39 democrats.

    So the committee has

    (C (58,3) * (C (39,2)) variants, or

    58! / (3!55!) * 39! / (2!37!)

    =30856*741

    =22864296
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