Monotone paths across a grid

MediumCombinatorics~4m

On a 6×66\times 6 grid of cells you start at the bottom-left corner (0,0)(0,0) and move only up or right along grid lines to the top-right corner (6,6)(6,6). How many distinct paths are there?

Show hints (2)+
  1. Each path is 66 ups and 66 rights in some order.
  2. Choose which of the 1212 moves are ups: (126)\binom{12}{6}.

Answer

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924

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Asked at: Jane Street, Optiver

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