# Math Help - Proving a binomial identity

1. ## Proving a binomial identity

Prove that:

$\binom{r}{k}=\frac{r}{r-k}*\binom{r-1}{k}$

Here is as far as I've gotten:

$r\frac{(r-1)!}{(r-1-k)!(k)!}$

which would be equal to
$r\binom{r-1}{r-k}$...i think
I'm stuck for the next step.

2. Originally Posted by chaotixmonjuish
Prove that:

$\binom{r}{k}=\frac{r}{r-k}*\binom{r-1}{k}$

Here is as far as I've gotten:

$r\frac{(r-1)!}{(r-1-k)!(k)!}$

which would be equal to
$r\binom{r-1}{r-k}$...i think
I'm stuck for the next step.
So

$\binom{r-1}{k}=\frac{(r-1)!}{k!(r-1-k)!}$

Now if we multiply by

$\frac{(r-1)!}{k!(r-1-k)!}\cdot \frac{r}{(r-k)}=\frac{r!}{k!(r-k)!}=\binom{r}{k}$

3. Well I'm stuck as to what to factor out to get the $\frac{r}{r-k}$. Im not too certain at all as to how the denomenator r-k comes into play.