Paths to work

This Riddler puzzle is a classic problem: how many lattice paths connect two points on a grid? Here is a paraphrased version of the problem.

The streets of Riddler City are laid out in a perfect grid. You walk to work each morning and back home each evening. Restless and inquisitive mathematician that you are, you prefer to walk a different path along the streets each time. How many different paths are there? (Assume you don’t take paths that are longer than required). Your home is M blocks west and N blocks south of the office.

Here is my solution:
[Show Solution]

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