SOLUTION: A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular?

Question 1020210: A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A garden has 15 slots for flowering pots. In how many ways can the pots be arranged if the garden is circular?

Solution:
We assume from the context of the question that the 15 pots are distinct, or different.
We further assume that only the ordering of the pots is important, i.e. the positions of the pots have no significance, just like ordering guests at a round table. They can be rotated and still considered the same arrangement.

This way, the position of the first pot is irrelevant. We will position the following pots in the clockwise direction, which gives 14! as the possible number of arrangements.

However, in my personal opinion, the position of the first pot in a garden is important, since a garden is rarely rotationally symmetrical. If that's the case, then there are 15! possible arrangements, taking "mirror" arrangements as different.
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