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Three coins are selected from 10 coins: 4 dimes, 4 nickels, and 2 quarters.

In how many possible ways can the selection be made so that the value of the coins is at least 25 cents?

I know that the total outcomes equals 120, but how do I find how many of these have the value of at least 25 cents?

  • math -

    The answer is 92. Anyone have idea how to solve this or why the answer is 92? Thanks in advance!

  • math -

    Consider the cases which do not add up to 25, they would be
    DNN and NNN
    DNN -- C(4,1)C(4,2) = 24
    NNN -- C(4,3 = 4
    so 28 cases are not allowed
    leaving 120 - 28 = 92

    another way:

    You have to list the possible outcomes , then evaluate each one, finally add up the allowable cases

    QQQ - C(4,1) = 4
    QQD - C(2,2)C(4,1) = 4
    QNN - C(2,1)C(4,2) = 12
    QDD - .... = 12
    QND - .... = 32
    DDD - .... = 4
    DDN - .... = 24
    DNN gives us < 25 cents
    NNN gives us < 25 cents.

    the total of the above is 92

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