Working with binomial identieies.

  • #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?
 

Answers and Replies

  • #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.
 
  • #3
Was that an actual proof of the identity?
 
  • #4
Dick
Science Advisor
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It would be if you write r instead of n in the original statement as Russell Berty pointed out.
 

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