3. For a $5 \times 5$ grid colored as follows, place 5 different rooks in the black squares, such that no two rooks can attack each other (rooks in the same row or column will attack each other). How many different ways are there to do this?

Place the rooks in the black squares of the grid, ensuring that no two rooks are in the same row or column.
【Answer】1440
【Analysis】Five rooks must be placed in rows $1 \sim 5$, one per row, and columns 1 and 5, one per column, to ensure they do not attack each other (similar to Sudoku). Rooks on black squares: Row 1 has 3 possible placements, Row 2 has 2, Row 3 (different from Row 1) has 2, Row 4 (different from Row 2) has 1, and Row 5 has 1, giving a total of: $3 \times 2 \times 1 \times 2 \times 1=12$ (ways). Different orders of the rooks: $5 \times 4 \times 3 \times 2 \times 1=120$ (ways). Therefore, the total is: $12 \times 120=1440$ (ways).