Two chess players, A and B, are going to play 7 games. Each game has three possible

Chapter 1, Problem 7

(choose chapter or problem)

Two chess players, A and B, are going to play 7 games. Each game has three possible outcomes: a win for A (which is a loss for B), a draw (tie), and a loss for A (which is a win for B). A win is worth 1 point, a draw is worth 0.5 points, and a loss is worth 0 points.

(a) How many possible outcomes for the individual games are there, such that overall player A ends up with 3 wins, 2 draws, and 2 losses?

(b) How many possible outcomes for the individual games are there, such that A ends up with 4 points and B ends up with 3 points?

(c) Now assume that they are playing a best-of-7 match, where the match will end as soon as either player has 4 points. For example, if after 6 games the score is 4 to 2 in favor of A, then A wins the match and they dont play a 7th game. How many possible outcomes for the individual games are there, such that the match lasts for 7 games and A wins by a score of 4 to 3?