没见过这种题目，属于哪一类呢？

Particle Man is at the origin in three-dimensional space. How many ways can Particle Man take a series of 12 unit-length steps, each step parallel to one of the coordinate axes, from the origin to (3, 4, 5) without passing through the point (2, 3, 2)? 

请不吝赐教！谢谢。