In how many different ways one can place 3 rooks on the cells of $6 \times 2006$ chessboard such that they don't attack each other?
In order not to attack each other, the rooks no to rooks can share a row or a column. Since there are 6 columns in total, we have 20 possibilities for choosing 3 columns in which we will place our rooks. After choosing the columns, we will place our rooks one by one in these columns. The first rook can be placed in 2006 different ways. The second one, however can't be placed in the row that contains the first rook. Hence there are 2005 possibilities for the second rook. Similarly, the third rook can be placed in 2004 different ways. In total, there are $20 \cdot 2006 \cdot 2005 \cdot 2004$ ways to place 3 rooks in $6 \times 2006$ chessboard so that they don't attack each other.