The rook is a chess piece that may move any number of spaces either horizontally or vertically. Consider  the “rooks problem” where we try to place 8 rooks on an 8x8 chess board in such a way that no pair  attacks each other.  a. How many different solutions are there to this? b. Suppose we place the rooks on the board one by one, and we care about the order in which we  put them on the board. We still cannot place them in ways that attack each other. How many  different full sequences of placing the rooks (ending in one of the solutions from a) are there?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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The rook is a chess piece that may move any number of spaces either horizontally or vertically. Consider 
the “rooks problem” where we try to place 8 rooks on an 8x8 chess board in such a way that no pair 
attacks each other. 
a. How many different solutions are there to this?
b. Suppose we place the rooks on the board one by one, and we care about the order in which we 
put them on the board. We still cannot place them in ways that attack each other. How many 
different full sequences of placing the rooks (ending in one of the solutions from a) are there?

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