Combinatorics · Product rule · Counting with restrictions · Indistinguishable objects · Combinations
In how many ways can a king, a queen, two rooks, two bishops and two knights be placed on the eight squares of the first rank of a chessboard so that the two rooks stand on opposite sides of the king, and one bishop stands on a white square while the other stands on a black square?
Two pieces of the same type (the two rooks, the two bishops, the two knights) are indistinguishable, and exactly one piece is placed on each square.
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Serbian Regional Competition (Okruzno takmicenje) 1997, high school grade I, problem 4. The 1997 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).