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In how many ways can 7 people { A, B, C, D, E, F, G...

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Basic Math

In how many ways can 7 people { A, B, C, D, E, F, G } be seatedat 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 sitbetween any of these three)?

(c) A and B must sit together, but neither can be seated next toC or D.

Consider each of these separately. For (c) you may NOT simplylist all possibilities, but must use the basic principles we havedeveloped (you may check your work with a list if you wish).

Hint: Conceptually, think of the groups of two or three peopleas one "multi-person" entity in the overall circular arrangement.However, a "multiperson" is an unordered entity, and you will haveto think about how many ways a "multiperson" could be ordered. Itmay help to draw a diagram, fixing a particular person at the topof the circle (thereby eliminating the duplicates due torotations).

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