Suppose that Novak Djokovic and Roger Federer are playing a

Suppose that Novak Djokovic and Roger Federer are playing a tennis match in which the first player to win three sets wins the match. Using D and F for the winning player of a set, in how many ways could this tennis match end?

Solution

the match must end in a maximum of 5 sets.

SIMPLIFICATIONS:

The first simplification is to consider only D winning and multiply by 2

The second is to consider as if all 5 sets are played. The rationale is that D is the winner whichever 3 out of 5 sets he wins.

The formula is simple, 5 choose 3 or 5C3 = 10

And another 10 for F winning,

10+10 = 20

20 WAYS THAT COULD END THIS TENNIS MATCH