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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, (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.)

 Jan 22, 2020
 #1
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Let's have the people be named 1,2,3,4,5 They could sit: 12345 23451 34512 45123 51234 or the reverse since order matters (12345 is different from 54321) There are 5! or 120 different ways the people can sit So 10/120 or 1/12 is the chance that they sit in ascending or descending order. 

 Jan 22, 2020
 #2
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There are 13 possible pairs: (6,0), (6,2), (6,4), (5,3), (5,2), (5,5), (3,3), (4,6), (3,5), (2,5), (4,4), (2,6), (0,6).

 Jan 23, 2020

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