The first World Series was played in 1903 and was a rare best of nine game format. Thus, the first team to win 5 games was declared the winner. As it turned out, the Boston Americans defeated the Pittsburgh Pirates in 8 games. The exact sequence of games was:
| Game 1 | Game 2 | Game 3 | Game 4 | Game 5 | Game 6 | Game 7 | Game 8 |
|---|---|---|---|---|---|---|---|
| P | B | P | P | B | B | B | B |
How many sequences like this are there where Team B beats Team P in 8 games of a 9 game series?
Since we want to find the sequences where Team B beats Team P in the 8th game, that means they have to win 5 games total including Game 8.
I set this up as:
@ksimmon1 I think that 8\choose5 includes, for example,
| Game 1 | Game 2 | Game 3 | Game 4 | Game 5 | Game 6 | Game 7 | Game 8 |
|---|---|---|---|---|---|---|---|
| P | B | P | B | B | B | B | P |
That series really would’ve ended in game 7
Instead of using the formula:
Would this formula work?
Because at Game 7, Team B would have had to win exactly 4 games before going into Game 8?
If this formula works the answer would be: