Point sequences that lead to deuce

In a tennis game the score climbs $0, 15, 30, 40$. In how many distinct orders of points won can a game reach $40$–$40$ (deuce) for the first time?

$20$. Reaching $40$–$40$ takes exactly six points, three to each player, and no game can end before then. Choosing which three of the six points the first player won gives $\binom63=20$.