- #1

m1sanch

- 3

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## Homework Statement

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.

## Homework Equations

1)Number of permutations with two types=(n choose n

_{1})=n!/((n

_{1}!)(n-n

_{1}1))

2)Number of ways to place n rooks which have k object types(colors) on n-by-n board=(n!)

^{2}/((n

_{1}!)(n

_{2}!)...(n

_{k}!))

## 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.