The grid is × where can be up to 1000. Each cell is either '.' (passable) or '*' (blocked). You start at (1,1) and want to reach (,). Since you can only move right or down, every path has exactly 2n-2 moves.
But not all combinations are valid because of blocked cells. The key constraint: if a cell is blocked, there are zero ways to reach it. And if you can't reach a cell, you can't use it to reach cells below or to its right.