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Suppose that the U.S. Senate consisted of 57 Republican and 43 Democratic Senators. How many different 12-person committees could be formed with 8 Republican senators and 4 democratic senators?

  • Math -

    C(57,8) x C(43,4) = ....

  • Math -

    Is the answer 2508.52
    and if so, how do I explane the whole solution. I am acting as a elementary teacher and have to discuss how to work each part out.

  • Math -

    the answer has to be a whole number, you can't have part of a committee, (although with most governments that is obviously possible)

    C(n,r) or nCr
    is defined as n!/(r!(n-r)!)
    and gives us the number of combinations of r things from n possibilites

    e.g. given A, B, C, D, how many combination of 2 letters can we form
    -we could list them AB, AC, AD, BC, BD, and CD
    -notice this would be C(4,2) = 4!/(2!2!)
    = 4x3x2x1/(2x1x2x1) = 24/4 = 6

    a number like C(57,8) is quite large
    around 1.6 billion
    and to do it on your calculator by just using the definition, will overload your calculator.

    Look for a key labeled something like

    test it on C(4,2)
    enter 4
    press 2nd nCr
    press 2
    you should get 6

    btw, the answer to your question is usually left in the notation I used, to express it in its full 15 digit number is rather futile.

    Are you doing this in elementary school?? Wow

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