Given a set containing N elements, how many different subsets are there that contain P elements? For P==0, the answer is always 1, the empty set.

Does that make it easier for you to understand? Update: Um, that sounds harsher than I intended it. For what it's worth, I found tilly's explanation hard to understand. I knew what he was getting at but the way he described there being only one possible choice of actions (no action) wasn't convincing to me, even leading me to thinking "there is no way to pick 0 things from 0 things because there is nothing to pick from". But changing terminology makes it very easy to understand, I think. The only choice I can make is to give you the empty set, the set that contains no items. So I'm not giving you zero sets, I am giving you one set.