# 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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