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 + 1, 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).
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