# chessboard problem with rooks

• June 5th 2012, 03:46 PM
blaydFaire
chessboard problem with rooks
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• June 5th 2012, 04:37 PM
Plato
Re: chessboard problem with rooks
Quote:

Originally Posted by blaydFaire
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.