Teams A and B play in a basketball tournament. The first team to win

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Pls suggest the solution

I’d love to see an algebraic Solution.

Since the numbers were reasonable, I “brute forced” the problem and luckily caught on to a pattern.

Rules:

win 2 in a row it is over

win 4 total it is over.


Start with the easiest scenario: 2 games

A - A
or
B - B


They could also play 3 games:

A - B - B
or
B - A - A


We can also have them play 4 games:

A - B - A - A
or
B - A - B - B


Since once we get 2 wins in a row the tournament ends, we can do 2 ways each for:

5 games
A - B - A - B - B
or
B - A - B - A - A


And 6 games
A - B - A - B - A - A
or
B - A - B - A - B - B


The tricky part is realizing there is 4 ways for the tournament to be played for 7 total games

Option 1: no team wins 2 in a row and the team who wins 1st ends up as the 4th win

A - B - A - B - A - B - A
or
B - A - B - A - B - A - B


Option 2: the team that wins 2nd, goes on to win the last 2 games for a total of 4

A - B - A - B -A - B - B
or
B - A - B - A - B - A - A


There are 14 ways the tournament can be played.

(B)

Posted from my mobile device

I followed the same approach but missed the last part about 7 games and got 12 as the answer. Now I know why.

If time is a consideration, since a given pattern of winning is available to each team means an even number of total ways, the answer choices can be reduced to just two

Posted from my mobile device