# Math Help - Proof regarding combinations

1. ## Proof regarding combinations

Show that:

(n choose 1) + (n choose 3) + ... = (n choose 0) + (n choose 2) + ...

I understand that the left side is all of the odd sized combinations from a set of n distinct objects and the right side is all of the even sized combinations from a set of n distinct objects, but I'm not exactly sure how to go about proving this.

Thanks.

2. Originally Posted by donald17
Show that:
(n choose 1) + (n choose 3) + ... = (n choose 0) + (n choose 2) + ...
$\left( {x + y} \right)^n = \sum\limits_{j=0}^{n} {\binom{n}{j}x^j y^{n - j} }$
Let $x=1~\&~y=-1$ look at the odd and the even terms.