HMMT 1999 A10

Pyramid $E A R L Y$ is placed in $(x, y, z)$ coordinates so that $E=(10,10,0), A=(10,-10,0), R=$ $(-10,-10,0), L=(-10,10,0)$, and $Y=(0,0,10)$. Tunnels are drilled through the pyramid in such a way that one can move from $(x, y, z)$ to any of the 9 points $(x, y, z-1),(x \pm 1, y, z-1)$, $(x, y \pm 1, z-1),(x \pm 1, y \pm 1, z-1)$. Sean starts at $Y$ and moves randomly down to the base of the pyramid, choosing each of the possible paths with probability $\frac{1}{9}$ each time. What is the probability that he ends up at the point $(8,9,0)$ ?