mathmatical analysis

This is for a math class I am taking I got the answer completely wrong on an already completed quiz.

In the game of chess, if white makes one move and black responds with one move, how many possibilities are there?

4000? >.>

White has 20 possible moves for its first choice and black has 20 possible responses so 20x20 = 400 possibilities.  :)

A much more interesting question is how many possibilities after two moves for each side, both in numbers of distinct positions and distinct games, which will be MUCH more difficult to answer.

Seems like a trick question. If it's from the starting position, then 400 would be right. But if it's in a different position than the initial, it could be anywhere from 1 possibility to an infinite amount.