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...

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?