How many sequences are possible in a seven-game World Series?
In other words, if two teams play the full seven games before one of them wins the required four games, how many different sequences of seven games are possible?

Extra Credit: How many different sequences are possible for any World Series (where it could end in four, five, six, or seven games)?


Solution:
The answer to the first question is 40 sequences!

Since each team must win 3 of the first 6 games, you can use the Combinations formula with 6 games taken 3 at a time. Then there are two possible winners for the seventh game.

It is best seen with a tree diagram or a table. Let A represent the American League Champion and let N represent the National League Champion. Listed below are the 40 different sequences possible:

Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Game 7
A A A N N N A
A A A N N N N
A A N A N N A
A A N A N N N
A A N N A N A
A A N N A N N
A A N N N A A
A A N N N A N
A N A A N N A
A N A A N N N
A N A N A N A
A N A N A N N
A N A N N A A
A N A N N A N
A N N A A N A
A N N A A N N
A N N A N A A
A N N A N A N
A N N N A A A
A N N N A A N
N N N A A A N
N N N A A A A
N N A N A A N
N N A N A A A
N N A A N A N
N N A A N A A
N N A A A N N
N N A A A N A
N A N N A A N
N A N N A A A
N A N A N A N
N A N A N A A
N A N A A N N
N A N A A N A
N A A N N A N
N A A N N A A
N A A N A N N
N A A N A N A
N A A A N N N
N A A A N N A

The answer to the extra credit is 70 sequences.



Correctly solved by:

1. Richard K. Johnson La Jolla, California
2. Keith Mealy Cincinnati, Ohio
3. Walt Arrison Philadelphia, Pennsylvania
4. Nick von Keller Winchester, Virginia
5. David Powell Winchester, Virginia
6. Geoff Keith Santa Monica, California
7. Renata Sommerville Austin, Texas
8. Matt Crandell Winchester, Virginia
9. Diana Xing Fort Collins, Colorado
10. Tony Wu Fort Collins, Colorado