In Mens Tennis the winner of a match is the person who wins

In Men\'s Tennis, the winner of a match is the person who wins a Best of 5 series of sets. That means that the series ends as soon as 1 player wins 3 sets. Two players, Stan and Novak, are playing in one of these series.

A) How many ways are there for the series to end in 3 sets?

B) How many ways are there for the series to end in 4 sets?

C) How many ways are there for the series to take the full 5 sets?

D) How many different ways are there for a Best of 5 series to end?

Solution

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A) For the series to end in 3 sets there seems to be only two possible ways, i.e. either Stan wins all 3 sets or Nova wins all 3 sets.

B) For the series to end in 4 sets, there seems to be six Possible ways(2X 3!/2!), i.e. 3 ways for Stan to win and 3 ways for Novak to Win.

typical sets

N S S S     &   S N N N

S N S S     &   N S N N

S S N S     &   N N S N

C) For the series to end in all five sets, there are (2 X 4!/(2!X2!)) 12 possible ways.

D) Maximum number of ways for best of five series to end, is 2^5= 32