Chess Combinatorics

How many ways can 8 identical \(\color {blue}{Rooks}\) be placed on a chessboard if each row must contain a \(\color {blue}{Rook}\), and that any given column may have 2 \(\color {blue}{Rooks}\) at most?

Details and Assumptions

  • For these purposes, the amount of \(\color {blue}{Rooks}\) in a column is all that matters in an arrangement.

*For example, the sample arrangement (\(R\) represents a \(\color {blue}{Rook}\)):

is the same as the sample arrangement:

  • Rows are from \(Left\) to \(Right\).
  • Columns are form \(Top\) to \(Bottom\).

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