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Homework Help: Probability Question

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data

    prove that
    [tex]\sum[/tex]nk=0 ([tex]^{n}_{k}[/tex]) ([tex]^{m-n}_{n-k}[/tex]) = ([tex]^{m}_{n}[/tex])

    2. Relevant equations
    2n=[tex]\sum[/tex][tex]^{n}_{k=0}[/tex] ([tex]^{n}_{k}[/tex])

    3. The attempt at a solution
    I know that every summand on the left hand side is a member of the power set times the combinations of it's complement and we can think of them in terms of the set changing with every possible combination, 1 element at a time and 2 at a time, 3 at a time, ..., n at a time. Or something like that... Definitely having trouble putting this into words let alone an equation. I certainly see the connection but am needing a little help on the proof. Please not the whole proof but just a little help putting it into words?
    Last edited: Sep 13, 2010
  2. jcsd
  3. Sep 12, 2010 #2


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    Gold Member

  4. Sep 13, 2010 #3
    Having some trouble getting my head around this still.
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