Ways to reach deuce

EasyProbability Combinatorics~3m

In tennis, points are scored $0 \to 15 \to 30 \to 40$ . How many distinct sequences of points lead to the score $40$ – $40$ (deuce) for the first time - i.e. both players reaching $40$ (three points each)?

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Deuce means each player won exactly $3$ points ( $6$ points total).
Count which $3$ of the $6$ points one player wins: $\binom63$ .

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Asked at: Optiver, Akuna Capital

Ways to reach deuce

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