Consider the moves
R: (x, y) → (x + 1, y) and U: (x, y)→ (x, y + 1), as in Example 1.42. In how many ways can one go
a) from (0, 0) to (6, 6) and not rise above the line y = x?
b) from (2, 1) to (7, 6) and not rise above the line y = x –1?
c) from (3, 8) to (10, 15) and not rise above the line y = x + 5?
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