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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

 May 29, 2020
 #1
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I counted them and got

6 of 1 and 0 of the other      (6,0)  (0,6)

5 of 1 and 1 to the other      (6,2)  (2,6)

4 of 1 and 2 of the other      (6,3)  (3,6)                  also (6,2)  (2,6) again

                                            (6,4)  (4,6)

                                             (5,2)  (2,5)

3 each                                  (5,5)

                                             (6,5)  (5,6)

                                             (3,3)

 

So I counted    14 possibilities

 Jul 4, 2020

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