Hello, I was able to find 252,252 for part "a" but I am having trouble finding the answer to "b." Any help would be great, thank you.

A hungry ant encounters a 3-dimensional lattice resting on the ground, having dimensions 5"5"4". The width of the lattice, running east-west is x = 5", the length, running northsouth is y = 5" and the height, running up-down is z = 4". One corner of the lattice is at the point (x, y, z) = (0, 0, 0) and the far corner, in an east, north, and up direction is (5, 5, 4). The ant encounters the lattice at (0, 0, 0) and will find chocolate at (5, 5, 4). The always efficient ant will reach the goal in 14 moves traveling only east, north, or up. If the ant randomly chooses the next lattice point toward its goal,[a] How many unique paths can it take to reach the chocolate?[b] What is the probability that the ant passes through (2, 2, 2) on the way to (5, 5, 4)?