(a) In how many ways can a particle move in the xy-plane from the origin to the point (7, 4) if the moves that are allowed are of the form:
(R): (x, y) †’ (x + 1, y); (U): (x, y) †’ (x, y + 1)?
(b) How many of the paths in part (a) do not use the path from (2, 2) to (3, 2) to (4, 2) to (4, 3) shown in Fig. 1.12?
(c) Answer parts (a) and (b) if a third type of move
(D): (x, y) †’ (x + 1, y + l)
is also allowed.

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