Problem
COM-B1-M11-P020 Not Through the Center
#20
★★★☆☆ Level 3 of 5
How many shortest paths from \((0,0)\) to \((4,4)\) do not pass through \((2,2)\)?
Subtract paths through \((2,2)\).
Total paths: \(\binom{8}{4}=70\). Through \((2,2)\): \(\binom{4}{2}\cdot\binom{4}{2}=36\). Hence the answer is \(70-36=34\).
Complement in grid paths.