Answer:
There are 35 ways.
Step-by-step explanation:
Consider the provided information.
In order to find the number of possible sequences we have few case:
Case I: If team A will win all 4 games without losing any match.
<u>A</u> <u>A</u> <u>A</u> <u>A</u>
There is only 1 way as you can see, Because after winning 4 games in a row no need to play again.
Case II: If team A will win 4 games out of 5 games.
<u>A</u> <u>A</u> <u>A</u> <u>B</u> <u>A,</u> or <u>A</u> <u>A</u> <u>B</u> <u>A</u> <u>A,</u> or <u>A</u> <u>B</u> <u>A</u> <u>A</u> <u>A,</u> or <u>B</u> <u>A</u> <u>A</u> <u>A</u> <u>A,</u>
Remember <u>A</u> <u>A</u> <u>A</u> <u>A</u> <u>B</u> this is not going to include.
That means there are 4 possible ways if team B win one match.
Case III: If team A will win 4 games out of 6 games.
It means team A needs to win 3 games from first 5 games so that after wining 6th match they win the tournament.
So the number of ways are
That means there are 10 possible ways if team B win two match.
Case IV: If team A will win 4 games out of 7 games.
It means team A needs to win 3 games from first 6 games so that after wining 7th match they win the tournament.
So the number of ways are
That means there are 20 possible ways if team B win three match.
Thus, the total number of ways are: 1 + 4 + 10 + 20 = 35
Hence, there are 35 ways.