1How many ways are there to put 8 black rooks on a chessboar

1,How many ways are there to put 8 black rooks on a chessboard, so none can attack each other?

2,How many ways are there to put 3 white rooks and 5 black rooks on the chessboard, so none can attack each other?

Solution

The answer is: \"Obviously there must be a rook in every row and every column. Starting with the bottom row, it is clear that the first rook can be put on any one of eight different squares (Fig. 1). Wherever it is placed, there is the option of seven squares for the second rook in the second row. Then there are six squares from which to select the third row, five in the fourth, and so on. Therefore the number of different ways must be 8