Combinatorics: Tennis Deuces

In a game of tennis, how many different sequences of point wins can lead to a score of 40 - 40 (deuce)? Consider that the score progression in tennis follows the order of 0, 15, 30, 40.

Answer

To reach a deuce, both players must win exactly 3 points each, leading to a score of 40 - 40. Since a total of 6 points are played (3 points by each player), the number of ways to reach this score can be calculated by choosing 3 winning points for one player out of the 6 points played. So

\[ \binom{6}{3} = 20. \]
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