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There are six people sitting at a circular table. Each person is either tall or short. Let a be the number of people sitting next to at least one tall person, and let b be the number of people sitting next to at least one short person. How many possible ordered pairs (a,b) are there? (For example, (a,b)=(6,0)  if all six people are tall, since all six people are sitting next to a tall person, and zero people are sitting next to a short person.)

 Mar 2, 2020
 #1
avatar+110169 
+2

 

 

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

 Mar 2, 2020
 #3
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+1

how do you get (6,5) or (5,6)? i dont think you can

Guest Mar 2, 2020
 #4
avatar+110169 
0

I think you are right.  (5,6) and (6,5) are out.

Thanks  laugh

Melody  Mar 2, 2020
 #2
avatar+158 
+1

thank you!!!

 Mar 2, 2020

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