how can you find the number of possible outcomes...?

Question

How can you find the number of possible outcomes of a playoff between 2 teams where the first team that wins 4 games wins the playoff???

Answer 1

Hello,

We assume that the series is 7 games. Then we have a permutation like AAABBBBA or a 7 letter word with 3 repeats and 4 repeats so we have 7!/[(3!)*(4!) = 35

Hope This Helps!

Answer 2

Since there are 2 teams, there are only 2 outcomes:

Outcome 1: Team A wins the playoff.
Outcome 2: Team B wins the playoff.

However, if you are asking about the number of ways to REACH those outcomes...

Team A wins 4 games - 1 possible way:
AAAA

Team A wins 4 games, team B wins 1 game - 4 possible ways, because A must win the last game:
BAAAA
ABAAA
AABAA
AAABA

Team A wins 4 games, team B wins 2 games - 10 possible ways, because team A must win the last game:
BBAAAA
BABAAA
BAABAA
BAAABA
ABBAAA
ABABAA
ABAABA
AABBAA
AABABA
AAABBA

Team A wins 4 games, team B wins 3 games - 20 possible ways, because team A must win the last game:
BBBAAAA
BBABAAA
BBAABAA
BBAAABA
BABBAAA
BABABAA
BABAABA
BAABBAA
BAABABA
BAAABBA
ABBBAAA
ABBABAA
ABBAABA
ABABBAA
ABABABA
ABAABBA
AABBBAA
AABBABA
AABABBA
AAABBBA

Add these up to get 35, then multiply by 2, because team B could win in the same way. So, there are 70 possibilities.