A chess board is an 8 by 8 grid. Suppose 8 pieces are randomly placed on the board, into distinct positions.

• What is the probability that no two pieces are in the same row or column?
• What is the probably that all 8 pieces can fit in the same 4 by 4 square? (For example, if all of the pieces are in rows 2 to 5 and columns 3 to 6, then they all fit in the same 4 by 4 square.)
• What is the expected number of rows and columns that contain no pieces?