We are given eight rooks, five of which are red and three of which are blue. In how many ways can the eight rooks be placed on an 8-by-8 chessboard so that no two rooks can attack one another.
I don't know how to start this problem. Can anyone help?
[Math] Chess combinatoric problem
combinatorics
Best Answer
If all $8$ rooks had the same color this would just give you a permutation matrix, of which there are $8!$. Given any of these permutation matrices we may simply choose $3$ of the rooks to change colors to blue, for a total of $8!\cdot\binom{8}{3}$