(a) In how many ways can one go from (0, 0) to (7, 3) if the only moves permitted are R: (x, y) → (x + 1, y) and U: (x, y) → (x, y + 1), and the number of U's may never exceed the number of R's along the path taken?
(b) Let m, n be positive integers with m > n. Answer the question posed in part (a), upon replacing 7 by m and 3 by n.