1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Combinatorics: r-Combinations on a Multiset
  1. Combinatorics and sets (Replies: 18)

Loading...