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Round table of directors

CombinatoricsEasy

$6$ distinct directors sit at a round table with $6$ identical chairs. A seating is the same as another if one is a rotation of the other, while a mirror image counts as different. How many distinct seatings are there?

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Hint

Fix one director to remove the rotations.

Solution

Rotations are identical, so fix one director in a chosen place.
The other $5$ directors can then be placed in the remaining chairs in any order.
This gives $5! = 120$ arrangements.
Hence the number of distinct seatings is $120$ .

Answer: $120$

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