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Working with binomial identieies.

  1. Apr 16, 2009 #1
    [tex]\binom{r}{k}=\frac{r}{r-k}\binom{n-1}{k}[/tex]

    I'm having problems proving this. However, here is my reasoning:

    when factoring out an r you get

    [tex]\frac{r*(r-1)!}{(r-k)!k!}[/tex]
    [tex]
    \frac{r}{r-k}*\frac{(r-1)!}{(r-k-1)!k!}
    [/tex]

    Is this proper reasoning?
     
  2. jcsd
  3. Apr 16, 2009 #2
    That looks good. I think there is a typo in the problem the way it is stated. What is n?!

    I think it should read (r-1)Ck on the right side, not (n-1)Ck.
     
  4. Apr 16, 2009 #3
    Was that an actual proof of the identity?
     
  5. Apr 16, 2009 #4

    Dick

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    Science Advisor
    Homework Helper

    It would be if you write r instead of n in the original statement as Russell Berty pointed out.
     
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