If all 17 games are played, all possible score sequences are determined by which games of the 17 player 1 wins.
So either player 1 wins the first game or he loses it, and the same goes for the other 16 games. Thus, there are two scoring possibilities for each game. Since the result of any one game is independent of the others, we can multiply the number of possibilities for each game together, and determine that there are 2^17 score sequences.
The other problem is a bit trickier, because we have to stop counting when one player reaches 9. Do you have any idea how to count the possibilities here?