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Homework Help: Combinatorics: r-Combinations on a Multiset

  1. Sep 12, 2011 #1
    1. The problem statement, all variables and given/known data
    How many r-combinations are there of a multiset S = {1*a1, infinity*a2,...,infinity*ak}?


    2. Relevant equations
    The number of r-combinations on a multiset with k objects and infinite repetition number: (r+k-1) choose (r), or (r+k-1) choose (k-1).
    The number of r-combinations on a multiset with k objects and finite repetition number is 1-to-1 with the number of positive integral solutions to x1 + x2 + ... + xk = r.


    3. The attempt at a solution
    I'm not sure how to solve this problem since there is a mix of infinite and finite supplies of k objects.

    The answer is (n+k-2) choose (k-2) + (n+k-3) choose (k-2)...
     
    Last edited: Sep 13, 2011
  2. jcsd
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