(Circular Permutations) In how many ways can 7 people { A, B, C,
D, E, F, G } be seated at a round table if
(a) A and B must not sit next to each other;
(b) C, D, and E must sit together (i.e., no other person can sit
between any of these three)?
(c) A and B must sit together, but neither can be seated next to
C or D.
Consider each of these separately.
Hint: Conceptually, think...