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Math Help - Combination Probability

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    Combination Probability

    There are 10 students and 7 teachers. Four members of the committee are to be choosen from them randomly. What is the probability of the committee having more than 1 students?

    I have been trying to use the n!/n!(n-r) formula, but I dont' know how to plug the things in properly. Please help!
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    There are 10 students and 7 teachers. Four members of the committee are to be choosen from them randomly. What is the probability of the committee having more than 1 students?

    I have been trying to use the n!/n!(n-r) formula, but I dont' know how to plug the things in properly. Please help!
    I think you should divide this problem into several cases.

    Exactly 1
    C(10,1)*C(7,3)/C(17,4)

    Exactly 2
    C(10,2)*C(7,2)/C(17,4)

    Exactly 3
    C(10,3)*C(7,1)/C(17,4)

    Exactly 4
    C(10,4)*C(7,0)/C(17,4)

    And add them up to get your answer.
    ----
    There is an easier way.
    Since we want either 1,2,3, or all 4.
    Find the probably of its negation, that is, 0.

    Hence,
    C(10,0)*C(7,4)/C(17,4)

    Then 1 (total probability) subtract this result.
    To get the same answer.
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