17. (3 points) Among the natural numbers less than 5000, the numbers that are divisible by 11 and have a digit sum of 13, there are $\qquad$ in total.
【Solution】Solution: (1) Sum of digits in odd positions $=12$, sum of digits in even positions $=1$, resulting in $3190, 3091, 4180, 4081$, a total of 4 possibilities.
(2) Sum of digits in odd positions $=1$, sum of digits in even positions $=12$. Resulting in $1309, 1408, 1507, 1606, 1705, 1804$, 1903; 319, 418, 517, 616, 715, 814, 913, a total of 14 possibilities.

Total $4+14=18$ possibilities.
Therefore, the answer is: 18.