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Five people are sitting around a round table. Let x be the number of people sitting next to at least one woman and y be the number of people sitting next to at least one man. How many possible values of the ordered pair (x,y) are there? (For example, (5,0) is the result if all 5 people are women.)

 Oct 4, 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)

3 each                                  (5,5)

                                             (6,5)  (5,6)

                                             (3,3)

 

So I counted    12 possibilities

 Oct 4, 2020

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