Celia Lucas

2022-06-28

World Series In the World Series the American League team 1A_2 and the National League team 1N_2 play until one team wins four games. How many different sequences are possible, if the sequence of winners is designated by letters (for example, NAAAA means that the National League team won the first game and the American League won the next four)?

aletantas1x

Assume that the country A team wins, then the possible sequences is:

1.The team A wins all the game from start AAAA then, the possible sequences is 1.

2.The team A wins all 4 games from 5 games NAAAA then, the possible sequences is 4, because N cannot be at 5th position.

3.The team A wins all 4 games from 6 games NNAAAA then, the possible sequences is 10, because N cannot be at 6th position.

4.The team A wins all 4 games from 7 games NNNAAAA then, the possible sequences is 20, because N cannot be at 7th position.

In next case both team wins 4 games each so neglect the condition.
The total combination for the country A team (A) wins is:
$1+4+10+20=35$
Similarly the total combination for the country A team (N) wins is also 35.
The total combination is:
$35+35=70$
Therfore, we can say that the possible number of sequences is 70.

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