a) In how many ways can one travel in the xy-plane from (0, 0) to (3, 3) using the moves R: (x, y) → (x + 1, y) and U: (x, y) → (x, y + 1), if the path taken may touch but never fall below the line y = x? In how many ways from (0, 0) to (4, 4)?
b) Generalize the results in part (a).
c) What can one say about the first and last moves of the paths in parts (a) and (b)?
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