(a) How many distinct paths are there from (- 1, 2, 0) to (1, 3, 7) in Euclidean three-space if each move is one of the following types?
(H): (x, y, z) → (x + 1, y, z);
(V): (x, y, z) → (x, y + l, z);
(A): (x, y, z) → (x, y, z + 1)
(b) How many such paths are there from (1, 0, 5) to (8, 1, 7)?
(c) Generalize the results in parts (a) and (b).