Mock AIME 1 2006-2007 Problems/Problem 15

15. Let $S$ be the set of integers $0,1,2,...,10^{11}-1$ . An element $x\in S$ (in) is chosen at random. Let $\star (x)$ denote the sum of the digits of $x$ . The probability that $\star(x)$ is divisible by 11 is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Compute the last 3 digits of $m+n$