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- Jun 5th 2012, 03:46 PMblaydFairechessboard problem with rooks
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- Jun 5th 2012, 04:37 PMPlatoRe: chessboard problem with rooks
Consider this: There are $\displaystyle \binom{5}{3}$ 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.