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Math Help - Number of ways of dividing things into groups...

  1. #1
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    Number of ways of dividing things into groups...

    Suppose I have n number of identical objects and I want to distribute them into k number of boxes there are
    ^n^+^k^-^1C_n ways to do so, with no constrains upon the number of balls in the boxes.

    Now if I have n non identical objects and k boxes what should be the number of ways to distribute the objects?
    Last edited by rickrishav; November 5th 2010 at 10:48 PM.
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  2. #2
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    There is a mistake in the first part. It should be ^{n+k-1}\mathcal{C}_{k-1}.

    For the second part it is just k^n.
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  3. #3
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    Re: Number of ways of dividing things into groups...

    And what are the number of ways of putting n objects of which r_1 are of one type, r_2 are of second type and so on, into k number of boxes.
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  4. #4
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    Re: Number of ways of dividing things into groups...

    Quote Originally Posted by rickrishav View Post
    And what are the number of ways of putting n objects of which r_1 are of one type, r_2 are of second type and so on, into k number of boxes.
    The question implies r_1+r_2=n~.
    \binom{r_1+k-1}{r_1}\binom{r_2+k-1}{r_2}
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