7. Place eight "Rooks" on an $8 \times 8$ chessboard, if none of them can "capture" each other, then the eight rooks are in a "safe state". There are $\qquad$ different safe states.
7. 40320 The first row has 8 ways to place, the second row has 7 ways, $\cdots$, and the last row has only one way. Therefore, the number of ways to place in a safe state is $8 \times 7 \times \cdots \times 1=40320$.