20. Player A and Player B play table tennis, and finally A wins with a score of $11: 6$. Find the number of score sequences in which A has been leading throughout the game.
20. According to the new table tennis rules, after the 16th ball, the score should be $10: 6$, so the number of score sequences where player A has been leading all the time equals the number of broken lines with endpoints $(1,1),(16,4)$ that do not intersect the $x$-axis, which is $C_{15}^{9}-C_{15}^{10}=\frac{2}{5} C_{15}^{6}$.