Final answer:
There are 40,320 ways to place eight pawns on an 8x8 chessboard so that exactly one pawn is in each of the eight rows and exactly one pawn is in each of the eight columns.
Step-by-step explanation:
On an 8x8 chessboard, there are 8 rows and 8 columns. We need to place exactly one pawn in each row and each column.
To solve this problem, we can start by placing the pawn in the first row.
There are 8 possible positions in the first row to place the pawn. Once we have placed the pawn in the first row, we move to the second row.
Since we cannot place another pawn in the same column as the first pawn, there are 7 possible positions in the second row to place the second pawn.
We continue this process for each row, reducing the number of possible positions by 1 for each subsequent row.
Therefore, the total number of ways to place the eight pawns is 8x7x6x5x4x3x2x1 = 40,320.