Consider the set of lattice paths from (0, 0) to (8, 8). You should know one quick formula for the cardinality of that set. However, counting a different way can lead to an interesting identity involving binomial coefficients. Notice that any path goes through exactly one of the points (0, 8),(1, 7),(2, 6), (3,5), (4,4), (5,3) ,(8, 0). Count the number of lattice paths that go through each of those 9 points - leave the expression in terms of binomial coefficients. Even more interesting is what you get if you generalize to a destination of (n, n), n 2 1. I am unsure of how to go about solving this problem in any way that makes sense, Was wondering if anyone here could help?

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