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1. 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.)

 

2. There are 18 chairs numbered from 1 through 18 around a circular table. How many ways can three people be seated, so that no two people are adjacent?

Thank you!

 Feb 15, 2020
 #1
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Sorry, just figured out number 2, so no need to work it out! Thanks.

 Feb 15, 2020
 #2
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Sorry everyone! I worked both of these out and got them correct, sorry for taking your time. No need to help me, have a good day!

 Feb 15, 2020

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