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Basic Combinatorics Question

  1. Jul 17, 2008 #1
    1. The problem statement, all variables and given/known data
    How many subsets S [tex]\subseteq[/tex] {1,2,...,21} are there if S is required to contain 5 odd integers and 6 even integers?

    2. The attempt at a solution
    I am having trouble breaking this one down. If the subsets contain 5 odd and 6 even, do they only contain 5 odd and 6 even? That would be 11 elements in the set. So the first element would have 11/21 chance of being odd, the second would have 10/20,... until 7/17 for the fifth. The sixth would have a 10/16 chance of being even, seventh a 9/15,...and the eleventh would have 5/11. Am I even going the right direction?
  2. jcsd
  3. Jul 17, 2008 #2
    In how many ways can you pick 5 odd integers? In how many ways can you pick 6 even integers?
  4. Jul 17, 2008 #3
    ([tex]\stackrel{11}{5}[/tex]) odd and ([tex]\stackrel{10}{6}[/tex]) even?
  5. Jul 18, 2008 #4
    Correct. And together?
  6. Jul 18, 2008 #5
    Thanks! I understand it now.
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