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In how many ways can Prince Harry and Duchess Meghan walk on a lattice from (0, 0) to (n, 2n) (where each step is either

In how many ways can Prince Harry and Duchess Meghan walk on a lattice from (0, 0) to (n, 2n) (where each step is either right or up)?

How many of the above walks pass through (5, 7) AND (8, 12) (assuming n ≥ 8)

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