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Two rooks that do not attack each other

countingchessboardrookscombinations

Two identical rooks are placed on distinct squares of an 8 by 8 chessboard.

  1. In how many ways can they be placed so that they do not attack each other (not in the same row or column)?
  2. In how many ways do they attack each other?
  3. What is the probability that two randomly placed rooks attack each other?
Show a hint

Place the first rook anywhere, then count the squares safe from it. Remember the rooks are identical, so each pair has been counted twice.

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Balls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingCatalan NumbersCounting: Permutations and Combinations

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