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(Paths through each cell)
Think recursively. To reach cell (i, j), you came from (i-1, j) or (i, j-1). The number of paths to (i, j) is the sum of paths to those two cells.
Base case: The top row and left column have only 1 path each (you can only move in one direction).
This is the sum rule in disguise. Paths from above OR paths from the left, but now you add them because they're distinct paths.
