Don't know if this is in the right section but....

I need to write up a bijective proof of this:

$\displaystyle n+1 \choose{k+1}$$\displaystyle = \sum_{m=k}^{n} $$\displaystyle m \choose{k}$

I don't understand how that equals. I need to write up a little story to explain it like... if you're planning a party for n people but you want to make sure you don't miss anyone, so you add +1 persons to it and you need to order k amount of pizza, but don't want to not have too little pizza so you add +1 pizzas which would be the same as.... the other side of the equation.

Please help!

Nicole