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Lattice paths through a checkpoint

EasyCombinatorics~3m

Moving only right or up on a grid, how many shortest paths run from (0,0)(0,0) to (5,5)(5,5) and pass through the point (2,3)(2,3)?

Show hints (2)+
  1. Split at the checkpoint: paths to (2,3)(2,3) times paths from (2,3)(2,3) to (5,5)(5,5).
  2. (52)×(53)\binom{5}{2}\times\binom{5}{3} - multiply, don't add.

Answer

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100

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Asked at: Probability & Market-Making, Timed Mental-Math & Sequences

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