The World Series in baseball continues until either theAmerican League team or t

Question

The World Series in baseball continues until either theAmerican League team or the National League team wins fourgames. How many different orders are possible (e.g. ANNAAAmeans the American League team wins in six games) if the seriesgoes -- A) Five games? B) Six games? C) Seven games? The World Series in baseball continues until either theAmerican League team or the National League team wins fourgames. How many different orders are possible (e.g. ANNAAAmeans the American League team wins in six games) if the seriesgoes -- A) Five games? B) Six games? C) Seven games?

Explanation / Answer

5 games 5 choose 4 = (4!)/(4!(5-4)!) = 5 x 2 = 10 possibilities-
6 games 6 choose 4 = (6!)/(4!(6-4)!) = 15 x 2 = 30 possibilities
7 games 7 choose 4 = (7!)/(4!(7-4)!) = 35 x 2 = 70 possibilities
If you are using the book "Probability and StatisticalInference 8th Edition", the answer in the back of the book isnot correct. They forgot to multiple by 2 to each nCr,there are two teams not one.
My mistake, the answer in the back is correct. I forgotto account for the winning of 4 before playing all games.
So since a team must win the last game to win theseries...
5 games 4 choose 3 = (4!)/(3!(4-3)!) = 4 x 2 = 8 possibilities-
6 games 5 choose 3 = (5!)/(3!(5-3)!) = 10 x 2 = 20 possibilities
7 games 6 choose 3 = (6!)/(3!(6-3)!) = 20 x 2 = 40 possibilities 5 games 4 choose 3 = (4!)/(3!(4-3)!) = 4 x 2 = 8 possibilities-
6 games 5 choose 3 = (5!)/(3!(5-3)!) = 10 x 2 = 20 possibilities
7 games 6 choose 3 = (6!)/(3!(6-3)!) = 20 x 2 = 40 possibilities

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