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Combinations n things not all different

  1. Apr 12, 2013 #1
    Is there any formula which gives the combinations for n things (taken r at a time, r being less than n) which are NOT ALL different?
    Say you have a total of n things and in those n things you have p things identical. Then you are required to select r things (r may be less or greater than p). Then what are possible ways of selecting r?
  2. jcsd
  3. Apr 13, 2013 #2


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    Since nobody has answered yet, I will post my less-than-ideal answer which is more of a way that you could approach it rather than a guaranteed way of getting at the right answer.

    You could first ask what the number of possible ways is, if you select [itex]0 \le k \le r[/itex] of the p identical ones and (r - k) of the non-identical ones. This should give you an expression involving loads of factorials that hopefully simplifies. Then sum over k = 0 to r (or k = 0 to p, if r > p).
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