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In a best-of-7 match A vs B, where the match will end as soon as either player has 4 points. 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.

Is it just 6 choose 3 (the last game must be a win, so choose which are the winning games in game 1-6)?

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    $\begingroup$ Sounds good to me. $\endgroup$ – David Nov 25 '14 at 4:26
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Yes. Your approach and reasoning is correct.

Out of the first 6 games, A has to win 3 matches without fail but in any order. The last game, as you mentioned, must also be won by A.

So we choose 3 from 6 which gives 20 possible outcomes.

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