- #1

nowimpsbball

- 15

- 0

## Homework Statement

In how many ways can eight identical rooks be placed on an ordinary 8x8 chessboard so that no two are in the same row or column? In how many ways, if each rook has a different color?

## Homework Equations

I looked at the equation n choose k (nck), but I don't know if that would work

## The Attempt at a Solution

I know each time you place a rook that the number of spaces to put the next rook goes down to the next perfect square...

(Choice, Available Places to put rook)

(1,64)

(2,49)

(3,36)

(4,25)

(5,16)

(6,9)

(7,4)

(8,1)

I thought it might be 64*49*36*...*1, but that seems like that would be too large a number over 1.625 billion...my intuition says that is way too big.

Any hints, tips, suggestions, answers for this problem? Am I thinking about it the right way? Thanks