This is a homework question, but I've clearly made a mistake that I can't point out...
Nadal and Federer play in a grand slam tournament. They have to win three sets to win. (Best of five). How many possible games are there?
There are 2 options with only three sets: NNN and FFF.
I figured that for the options with 4 sets, e.g. NNFN or FNFF.
I did 4C3 - 2, because NNNF and FFFN are not possible. 4C3 - 2 = 2
Then there are also the games with 5 sets, like NNFFN or FNFNF.
I figured that this should be 5C3 - 4, because NNNFF, FNNNF, FFFNN, NFFFN are not possible. This gives me 6.
All of this added up is 11. The answer book said 20. I can't figure out where I messed up.