Combinatorics in chess

Probability Level 3

How many ways are there to place a white rook and a black rook (on a standard 8x8 chessboard) such that they do not attack each other?

1098. 3136 4125 49

Pinaki Biswas by Pinaki Biswas , 45, India

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1 solution

Kellen Atkins
May 28, 2018

For each of the 64 options for the first rook we have 63 options for the second, minus the 2 ∗ ( 8 − 1 ) 2*(8-1) where it would attack the first (7 for the horizontals and 7 for the verticals), so we have 64 ∗ ( 63 − 14 ) = 3136 64 * (63-14) = 3136

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