SOLUTION: In a certain men's tennis tournament, two finalists, A and B, are competing for the title, which will be awarded to the first player to win four sets. In how many different ways ca

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Question 1186574: In a certain men's tennis tournament, two finalists, A and B, are competing for the title, which will be awarded to the first player to win four sets. In how many different ways can the match be completed?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) A winning in 4 sets:

AAAA
number of ways: 1

(2) A winning in 5 sets:

(AAAB) in some order, followed by A
number of ways: "4 choose 1" = 4

(3) A winning in 6 sets:

(AAABB) in some order, followed by A
number of ways: "5 choose 2" = 10

(4) A winning in 7 sets:

(AAABBB) in some order, followed by A
number of ways: "6 choose 3" = 20

Total number of ways for A to win: 20+10+4+1=35

Total number of ways for B to win (by symmetry): 35

ANSWER: 35+35=70 ways to complete the match