# Help the grasshopper

**Discrete Mathematics**Level 2

A 10 X 10 X10 cube is formed of small unit cubes. A grasshopper sits in the center O of one of the corner cubes. At a given moment it can jump to the center of any of the cubes which has a common face with the cube where it sits, as long as the jump increases the distance between point O ant the current position of the grasshopper. How many ways are there for grasshopper to reach the unit cube at the opposite corner?

answer is in the form \( \frac{a!}{b!^{c}}\)

Find \( a + b + c\)