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Math Help - Permutation

  1. #1
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    Permutation

    Hi, I need help with this permutation problem. Can anyone please explain how to solve this problem in steps? Thanks in advance.

    Q: In how many different ways can 5 pennies, 4 nickels, and 6 dimes be given to 15 children so that each child receives exactly 1 coin?
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  2. #2
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    Quote Originally Posted by Unknown View Post
    Q: In how many different ways can 5 pennies, 4 nickels, and 6 dimes be given to 15 children so that each child receives exactly 1 coin?
    Note that we have only 15 coins.
    Think of the children’s listed on a roster such as a roll book.
    How many ways can we list 5 P’s, 4 N’s and 6 D’s next to those names?
    Here is a hint: We can arrange the string “000111122222” in \frac{{12!}}{{\left( {3!} \right)\left( {4!} \right)\left( {5!} \right)}}.
    Last edited by Plato; August 18th 2008 at 02:05 PM.
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  3. #3
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    I'm not sure if I'm doing this right, but would the setup for the problem be 15!/6!5!4! ...?

    Because in total there are 15 to choose from and there are 3 different types of coins with a different value for each.

    So would the answer be 630,630?
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  4. #4
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    Quote Originally Posted by Unknown View Post
    I'm not sure if I'm doing this right, but would the setup for the problem be 15!/6!5!4! ...?
    So would the answer be 630,630?
    Correct.
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