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Multinomial coefficient

  1. Apr 28, 2013 #1
    Okay I got to wonder about this: Why is the multinomial coefficient independent of if you start by taking out n1, n2, n3 etc. or n2,n1,n3 or n3, n2, n1... etc.. I mean intuitively from actually doing the combinatorics by counting it seems obvious that the order should not matter. But can this be proved or is it taken as an axiom?
  2. jcsd
  3. May 2, 2013 #2
    Because no matter how you word it, it is the number of ways to partition a set of size N into subsets with respective sizes n1, n2, ..., nk. And there is no "ordering" of the subsets, so you interpret it in any order you like.
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