# Math Help - Combinatorical Identity

1. ## Combinatorical Identity

I've been thinking on this problem for 2 days but I haven't found even a clue. The question is to prove the correctness of the following identity:
$\displaystyle \sum _{k=0}^{p} {p\choose k}^{2}{n+2\,p-k\choose 2\,p}= {n+p\choose p} ^{2}$
Could you give me a hint about how to prove this?

2. Using mathematical induction I guess would be the easier way.

3. Originally Posted by p0oint
Using mathematical induction I guess would be the easier way.
Yes I know, but I think it's hard to use induction because it has power. BTW, it has two variables. I don't know how to use induction when there are two variables.

EDIT: I think it can be solved with double counting. But I don't what I should count in two different ways.