In a World Series, team A and B play each other until one team wins 4 games.?

Question

For example, the symbol ABBAAA represents a 6-game series in which A wins games 1,4,5, and 6.

a) Explain why there are C(5,3) different 6-game series won by Team A

b) Without listing, show that there are 70 different sequences possible

i really dont know how they got 70. i got an answer for a but not entirely sure if its correct

Answer 1

PART A:

How many ways are there to get to the point where team A has won 3 games in 5 games?  That would be C(5,3).  Then you just have them win the 6th game and you are done.

Thus C(5,3) = 20 would be the number of ways for team A to win after 6 games.

PART B:

To win the series, team A can win after 4 games, 5 games, 6 games or 7 games.

To win 4 games, they would have to win all 3 prior games.

C(3,3) = 1 way

To win 5 games, they would have to win 3 of the prior 4 games.

C(4,3) = 4 ways

To win 6 games, they would have to win 3 of the prior 5 games (see part A):

C(5,3) = 20 ways

To win 7 games, they would have to win 3 of the prior 6 games:

C(6,3) = 120 ways

That's 145 sequences that end with A winning.  There would also be 145 sequences that end with B winning.

Okay, I really don't know what they are saying about 70 game sequences.