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Math Help - chessboard problem with rooks

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    chessboard problem with rooks

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    Last edited by blaydFaire; June 5th 2012 at 05:54 PM.
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    Re: chessboard problem with rooks

    Quote Originally Posted by blaydFaire View Post
    In how many ways can 3 indistinguishable rooks be set on a 5 X 5 chessboard so that:
    a)only 2 rooks can attack each other
    Consider this: There are \binom{5}{3} ways to select the rows for the three rooks.
    Now order the rows from least to most.
    There are five ways to place a rook on the least numbered row.
    There are four ways to place a rook on the next numbered row in a non-attacking position.
    There are three ways to place a rook on the last numbered row in a non-attacking position.
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