In a two-team basketball play-off, the winner is the first team to win m games. (a) Counting

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In a two-team basketball play-off, the winner is the first team to win m games.

(a) Counting separately the number of play-offs requiring m, m+1,..., and 2m−1 games, show that the total number of different outcomes (sequences of wins and losses by one of the teams) is


(b) How many different outcomes are there in a “2 out of 3” play-off, a “3 out of 5” play-off, and a “4 out of 7” play-off?

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