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Math Help - questions in combination - help!!!

  1. #1
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    questions in combination - help!!!

    1. how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes

    2.how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes that every box have at least 1 ball

    3.how many posibilities to divide 10 identical white balls and 10 mixed color different balls to five different boxes

    please help me solve it, and please give details in the solution way
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  2. #2
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    Quote Originally Posted by tukilala View Post
    1. how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes

    2.how many posibilities to divide 10 identical white balls and 10 identical black balls to five different boxes that every box have at least 1 ball
    There {{N+k-1}\choose N} ways to place N identical objects into k different cells.
    For your balls, N=10 and k=5.
    You need to square the number for one colour. WHY?

    There {{N-1}\choose {N-k}} ways to place N identical objects into k different cells with no empty cell.
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