A walk in the positive quadrant of the plane consists of a sequence of moves, each one

Question:

A walk in the positive quadrant of the plane consists of a sequence of moves, each one from a point (a, b) to either (a + 1, b) or (a, b + 1).

(a) Show that the number of walks from the origin:x+y\ (0,0) to (x, y) is (

(b) Suppose a walker starts at the origin (0, 0) and at each discrete unit of time moves either up one unit or to the right one unit each with probability 1/2. If x > y, find the probability that a walk from (0,0) to (x,y) always stays above the main diagonal.

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