suppose you have standard 8oy8 chessboard and you place a ma

suppose you have standard (8-oy-8) chessboard, and you place a marker on the bottom left square, which we\'ll call (1, 1). Your marker can now take single moves: either the marker can move one square to the right, or one square upward at any step. Thus, it will take 14 moves to get the marker to the upper right corner, which we\'ll call (8, 8)

Solution

Total number of paths from (1,1) to (8,8) = 8!

Number of paths that lead from (1,1) to (3,3) = 3!

Number of paths that lead from (1,1) to (6,6) = 6!

Number of paths that lead from (3,3) to (8,8) = 6!

Number of paths that lead from (6,6) to (8,8) = 3!

Thus total number of paths from (1,1) to (8,8) without landing on (3,3) and (6,6) = 8! - 3! - 6! - 6! - 3! = 38868