Another Colorful Rooks!
Probability
Level
3
How many ways can a red rook, two orange rooks,two blue rooks, and three yellow rooks be placed on an 8 by 8 board such that they are not attacking each other?
The answer is 67737600.
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1 solution
8 rooks such that no one attacks each other and since 8×8 chess board this implies that all the rooks must be placed at diagonals of the chess board since the rooks attack vertically or horizontally, The no of ways in which 8 rooks can be arranged out of which 3 are alike of one kind 2 are alike of other kind and 2 are alike of other= 8!/(2!×2!×3!) = 8×7×6×5=1680