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Math Help - Distributing different objects

  1. #1
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    Distributing different objects

    Hi Guys,

    I need a little help with this problem.

    In how many ways can 10 different books be distributed among 20 people if each person can get any number of books.

    I can do 10 books among 20 people, 1 each, but the condition with any number of books is confusing me. How should I proceed?

    Thanks for your help.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by mathguy80 View Post
    Hi Guys,

    I need a little help with this problem.

    In how many ways can 10 different books be distributed among 20 people if each person can get any number of books.

    I can do 10 books among 20 people, 1 each, but the condition with any number of books is confusing me. How should I proceed?

    Thanks for your help.
    The first book can go to any of the 20 people. Similary for the second, third, ... and tenth books.

    The number of ways is 20\times20\times ...\ (10\ times)=20^{10}.
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  3. #3
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    Quote Originally Posted by alexmahone View Post
    The first book can go to any of the 20 people. Similary for the second, third, ... and tenth books.

    The number of ways is 20\times20\times ...\ (10\ times)=20^{10}.
    Thanks @alexmahone. That checks out.
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