I don't know how to solve this probability question, at first I thought it was a Bernoulli Random Variable question, but it's not. I mean, this is more like counting... but I don't know how to solve it... Can anyone help me? Here's my question:

Consider a backgammon match with 17 games, each of which can have one of two outcomes: win (1 point), or loss (0 points). Find the number of all possible distinct score sequences under the following alternative assumptions.

All 17 games are played.

The match is stopped when one player wins more than half the games.