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?