In how many ways can you color one cell blue and one cell red in the grid below so that the colored cells are not neighbors? Two cells are neighbors if they touch at all, even diagonally. (this is on a 5x5 grid)

So far, I have attempted to do this problem, but I'm afraid my answer is wrong. I tried to do casework calculations, starting with the corners, then the rows that did not get counted yet, then the columns that did not get counted yet. I added them up and got 399. I doubled that number because you can choose whichever color you want to do first. My final answer was 798. But I realized that some answers would overlap, so just doubling would not work. Does any of you have any ideas, or how I could get rid of the doubling?

Thank you for your time and effort, which are greatly appreciated, especially during these turbulent times.

Guest Apr 29, 2020