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

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)?

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

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

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Expert Solution

milcah answered 8 months ago

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