# Working with binomial identieies.

1. Apr 16, 2009

### chaotixmonjuish

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

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

when factoring out an r you get

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

Is this proper reasoning?

2. Apr 16, 2009

### Russell Berty

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. Apr 16, 2009

### chaotixmonjuish

Was that an actual proof of the identity?

4. Apr 16, 2009

### Dick

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