Solution to the Problem:
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:
| Gm 1 | Gm 2 | Gm 3 | Gm 4 | Gm 5 | Gm 6 | Gm 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.
