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Math Help - distribution (combinations) problem ...

  1. #1
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    distribution (combinations) problem ...

    Hello,

    I have a small problem/puzzle to solve which goes as follows:
    (I have already calculated it, however I am not sure I followed the right reasoning as mathematics is not my strong point and after building a Java app to brute force it, it crashed on out-of-memory error):

    ------------------------------

    We have ten bikes (b1, b2, , b10) that need to be sold at 3 shops
    houses (s1, s2, s3). Each shop can sell at most 5 bikes.

    How many solutions are possible? You may solve this using
    mathematics, or brute force with a spreadsheet, or small program.

    This is a problem in combinations where the order of selection does not matter.
    Selecting r things from n: nCr = n! / (r! (n-r)!)

    --------------------------------

    According to my math calc's there's 10! permutations of bikes (http://www.wtamu.edu/academic/anns/m...tut56_perm.htm), but I am not entirely sure where to take it after that ...

    Any advice would be much appreciated !

    hg
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  2. #2
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    Re: distribution (combinations) problem ...

    Quote Originally Posted by holyGrill View Post
    We have ten bikes (b1, b2, , b10) that need to be sold at 3 shops
    houses (s1, s2, s3). Each shop can sell at most 5 bikes.
    How many solutions are possible?
    There are several ambiguities here.
    Are the bikes all different? Or are they identical?
    Can there be a store which gets no bike at all?
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