Final answer:
The number of ways 8 rooks can be placed so that none are attacking is 40320.
Step-by-step explanation:
The correct answer is B) 40320.
In chess, a rook can move horizontally or vertically on the board. To ensure that none of the rooks are attacking each other, we need to place them in such a way that no two rooks are in the same row or column.
We can think of the problem as placing each rook in a different column. The first rook can be placed in any of the 8 columns. Once the first rook is placed, the second rook can be placed in any of the remaining 7 columns. This process continues until all 8 rooks are placed, resulting in a total of 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320 ways to place the rooks.