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Given 2n objects, number of ways to select n objects

  1. Feb 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Given N identical objects and N additional objects that are different from these and from each other, find the number of ways to select n objects out of these 2N objects.

    2. Relevant equations
    Either P(n,k) or C(n,k) or n^k or maybe even (n+k+1)/k

    3. The attempt at a solution
    Looking at these...so half the set is identical and the other half is distinct from the first half and from them selves. So I will call the first set S and the second set T to help me keep them apart.
    So for the first set everything is identical and w can select up to N of them... my notes seem to indicate i would go about it as (S+N+1)/N and then the second set they are distinct from each other and we can select N of them, so T^N? Are those two formulas in the right direction? If so would I multiply those together to get the correct answer?
  2. jcsd
  3. Feb 4, 2008 #2
    Just count them. Number of ways to select n of A, 0 of B is 1.
    n-1 of A, 1 of B is n
    n-2 of A, 2 of B is n(n-1), etc.

    So you get sum{i=0..n}(n choose i) = 2^n.
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