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  3. a quotforward pathquot in the plane is a sequence of...

Question: a quotforward pathquot in the plane is a sequence of...

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A forward path in the plane is a sequence of steps of the form (1,0) and (0, 1) (a) How many forward paths are there from (0,0) to (a, b) where a, b are non-negative b) How many forward paths are there from (a, b) to (c, d) where c 2 a 2 0 and (c) Generalize this definition to d dimensions by only allowing steps which increase integers? d 2b2 0 are integers? one of the coordinates by 1 (so (1,0,0 ,0), (0,1,0,...,0),... , (0,0,0,.,1)) How many forward paths are there from (0,0,...,0) to (a1, a2,... , ad) where a1,..., ad are non-negative integers?

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