Sets and Counting- World Series

Mathematics
Tutor: None Selected Time limit: 1 Day

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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