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Team A and Team B play each other in a best out of 7 tournament. So the team that wins 4 games first wins the tournament. How many possible sequences are there for team A to win? Examples: AAAA, AAABA, AABAA, etc.

Respuesta :

gcosarinsky

Answer: There 64 possible sequences in which team A wins

Step-by-step explanation:

Hi!

The sequences in which team A wins, are the ones with at least 4 A's.

Sequences with 4, 5, 6 or 7 A's. To calculate how many of each type exist, we use the formula of combinations. If you select K objects from a set of N objects, there are C(N, K) possibilities, give by the formula:

[tex]C(N,K) = \frac{N!}{K! (N-K)!)}[/tex]

Then the total M number of sequences in which team A wins is:

[tex]M = C(7,7) + C(7,6) + C(7,5) + C(7,4) = 1 + 7 +21+35 = 64[/tex]

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