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 don’t 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?