In how many different ways can you place the black rook and the black king if they must be next to each other (in any direction including diagonally). The two first diagrams show acceptable positions whereas the third one is not acceptable because there is at least one empty square between the rook and the king.
Here is what I have so far:
Black king in the corners-> 4 possible choices
Black king on the sides not a corner->24 possible choices
Black king on the interior->30 possible choices
I want to know if I am on the right track?