227. How Many Orderings

Print how many different orders n distinct items can be arranged in.

Reason about the choices. There are n items that could go first. Whichever you pick, there are n-1 left for the second position, and so on. Multiplying those choices together gives the answer.

This is the size of the search space every permutation-generating backtracking program has to walk, which is why they become impossible so quickly: at n = 20 there are more orderings than a computer could enumerate in a lifetime.

Constraints - `1 ≤ n ≤ 20`