Problem
COM-B1-M01-P016 Path Avoiding a Forbidden Point
#16
★★★☆☆ Level 3 of 5
How many shortest paths from \((0,0)\) to \((4,3)\), using only right and up moves, do not pass through \((2,1)\)?
Count all paths and subtract the paths through \((2,1)\).
There are \(35\) paths in total: choose the positions of three up moves among seven. Through \((2,1)\): \(3\) paths to the point and \(6\) paths from it to \((4,3)\). Forbidden paths: \(18\). Answer: \(35-18=17\).
Good complement example on a grid.