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Math Help - Choosing items from different types with restirctions.

  1. #1
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    Choosing items from different types with restirctions.

    A store sells 5 different types of office supplies: pencils, mechanical pencils, pens, erasers, and highlighters. How many ways are there to choose:

    a) 20 supplies?

    b) 20 supplies with at least one of each office supply?

    c) 20 supplies with at least 4 erasers and 2 pens?
    Last edited by mr fantastic; September 3rd 2011 at 12:30 AM. Reason: Re-titled.
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  2. #2
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    Re: Probability question

    Think hard. You probably have the tools.

    I like part B. Can you reduce the problem by simply picking one of each of the supplies and then worrying about how to choose 15 with no additional restriction?
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  3. #3
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    Re: Probability question

    would a be 5*4^19?
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  4. #4
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    Re: Probability question

    Quote Originally Posted by bjnovak View Post
    would a be 5*4^19?
    No, not even close.
    The number of ways to put N identical objects into K different cells is:
    \binom{N+K-1}{N}~.

    In your problem part a) the choices are identical, N=20.
    The supplies are different, K=5.

    For b) use reply #2 so N=15.
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