There is a cube of size $10 \times 10 \times 10$, consisting of small unit cubes. In the center $O$ of one of the corner cubes sits a grasshopper. The grasshopper can jump to the center of a cube that shares a face with the one it is currently in, and in such a way that the distance to point $O$ increases. In how many ways can the grasshopper jump to the cube opposite the initial one?
The grasshopper must make a total of 27 jumps - 9 in each direction. Let's denote the directions by the letters $A, B$, and $C$. Each path is uniquely determined by a sequence of length 27, in which the letters $A, B$, and $C$ each appear 9 times.

## Answer

$\frac{27!}{(9!)^{3}}$ ways.