Question 28

Consider an 8 $$\times$$ 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

Solution
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For each row, a rook can be placed in one of the eight cells. Once a rook is placed in a column, in no other row can a rook be placed in the same column. 

So, in other rows to place the second rook, there will be seven ways. Once the second rook is placed, there will only be 6 for the next row.

This way, the total ways = 8*7*6*5*4*3*2*1 = 8!

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