8 directors, the vice chairman and the chairman are to be seated around a circular table. If the chairman should sit between a director and the vice chairman, in how many ways can they be seated?

Answer: 8! * 2

Explanation: Let us consider the vice chairman and the chairman together as one entity. Hence, 8 directors + this entity can be arranged circularly in (9-1)! ways. However, the chairman and the vice chairman can interchange positions. This can be done in 2 ways. Hence the total number of ways in which they can be seated is 8! * 2.

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