Eight rooks are placed on a chessboard at random. Ten squares on
the chessboard are marked.
What is the probability that they are all in marked places?
total number of small squares = 64
No of ways 8 rooks are placed in the chess board = 64C8
No of ways 8 rooks are placed on the marked places of the chess board = 10C8
So, Desired probability = 10C8 / 64C8 = 1.016e-08
** If the answer does not match please comment.
Eight rooks are placed on a chessboard at random. Ten squares on the chessboard are marked....
Eight rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other rooks? Translation for those who are not familiar with chess: pick 8 unit squares at random from an 8 × 8 square grid. What is the probability that no two chosen squares share a row or a column? Hint. You can think of placing the rooks both with or without order, both approaches work.
4. If 8 rooks (castles) are randomly placed on a chessboard, compute the probability that none of the rooks can capture any of the others. That is, compute the probability that no row or file contains more than one rook.
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