(a) In how many ways can one travel in the xy-plane from (1, 2) to (5, 9) if each move is one of the following types:
(R): (x, y) → (x + 1, y); (U): (x, y) (x, y + 1)?
(b) Answer part (a) if a third (diagonal) move
(D): (x, y) → (x + 1, y + 1)
is also possible.