Six people are sitting around a circular table, and each person has either blue eyes or green eyes. Let $x$ be the number of people sitting next to at least one blue-eyed person, and let $y$ be the number of people sitting next to at least one green-eyed person. How many possible ordered pairs $(x,y)$ are there? (For example, $(x,y) = (6,0)$ if all six people have blue eyes, since all six people are sitting next to a blue-eyed person, and zero people are sitting next to a green-eyed person.) I got 14 and 8 but it said it was wrong. I need help
Please this is my 3rd time asking this question. It would mean a lot. Thank you for your time!!!
You can just brute force this one:
Adding up the bolded numbers, we get a final answer of 12 ordered pairs.
Hope this solutions helps!