Hi! I've tried about eight times on this problem, submitted it, and got all of them wrong. I need help on this. Can someone please explain this problem to me? Thanks!
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.)
Again, thank you so much.
(They gave me a hint to use casework, but I'm not quite sure how to use casework here.)