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# Counting and Probability question

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Six people are sitting around a circular table, and each person has either blue eyes or green eyes. Let  be the number of people sitting next to at least one blue-eyed person, and let  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'm somewhat confused on how to approach this question, could someone please guide me through it?

Thanks :D

May 25, 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

May 25, 2020
#2
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That was quite informative, thank you!

May 25, 2020
#3
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