Sets and Counting- World Series

label Mathematics
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schedule 1 Day
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In the world series, the american league team ("A") and the national league team ("N") play until one team wins four games. Each sequence of winners can be designated by a sequence of As and Ns. For instance, NAAAA means the National League won the first game and lost the next four games. In how many ways can a series end in seven games? Six games?

Apr 8th, 2015

There are 2^7 = 128 possible outcomes for a series of seven games and 2^6 = 64 outcomes for a series of six games.

Apr 8th, 2015

If the series ends after either of the teams wins 4 games, then for 7 games there are the following options:

4 "N" and 3 "A" -    *N*N*N*N  - 64 options because any of the As may be inserted in any of the places marked by *.

So, a series of 7 games may end with the victory of N  in 4*4*4 = 64 options.

Adding the same number for the victory of A we get that the series of  7 games may end in 128 different ways.

If a series ends after 6 games, then the total number of options is 2*16=64


Apr 8th, 2015

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Apr 8th, 2015
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