1. The problem statement, all variables and given/known data How many ways can two red and four blue rooks be placed on an 8-by-8 chessboard so that no two rooks can attack one another. 2. Relevant equations 1)Number of permutations with two types=(n choose n1)=n!/((n1!)(n-n11)) 2)Number of ways to place n rooks which have k object types(colors) on n-by-n board=(n!)2/((n1!)(n2!)...(nk!)) 3. The attempt at a solution With the two equations on top I thought that they answer would be (8 choose 6)((8 choose 6) choose 2)) since it will be a 6 rooks on an 8-by-8 board. *(8 choose 6)=(8!)/(6!((8-6)!)=8x7/2=28 This will simply to: 28(28!/(2!(28-2)!)= 28(28x27/2)= 14x28x27=28x27x14. Did I do this correct or am I wrong in my reasoning. P.S. I am sorry for the format. I am new to this site and tried to make it as clean as possible.