We adopt the convention that 0! = 1. This is done in order to simplify
the statements of certain theorems. One useful fact to note about *n*!is that
*n*! = *n*(*n*-1)!. Similarly,
*n*! = *n*(*n*-1)(*n*-2)!. This observation
allows some useful cancellation to take place when computing formulas
involving factorials.

The numbers ``*n* choose *k*'' occur all the time in counting problems
because we frequently are choosing *k* objects in such a way that a
given object may occur at most once (distinctness), and the order in
which the objects are chosen is irrelevant. For example, when being
dealt a hand of 5 cards, our main concern is with the final hand and
not in the order in which we receive the cards. It is true that we
may develop some anxiety as a hand develops if we watch each card
as it arrives in our hand, but in analyzing our chances of winning
the particular game, we start with the composition of the hand and do
not consider the order in which they arrived.

The word partition makes sense for the previous concept because the set is being broken into non-empty pieces which have no overlap. This is one of the colloquial uses of the word partition as well.