Counting Paths through a Grid

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A downward path joins the top spot A to the variable bottom spot B. For a fixed B, there are " choose " = possible paths, where is the row number and counts how far B is along its row, with both and starting at zero. These numbers are the binomial coefficients that form Pascal's triangle.

Contributed by: George Beck and Rob Morris (March 2011)
Open content licensed under CC BY-NC-SA


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