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How many shortest lattice paths start at (3, 3) and a. end at (15, 15)? b. end at (15, 15) and pass through (5,9)?

How many shortest lattice paths start at (3, 3) and a. end at (15, 15)? b. end at (15, 15) and pass through (5,9)? c. end at (15, 15) and avoid (5,9)? 31

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