Arrangements

Presumably for finding the number of different arrangements in circular situations we subtract 1 from the whole number. For example, to find out in how many ways 4 people can sit around a circular table we should say: 4-3, and then the answer would be 3!.

However, that doesn’t work for 3 people, because there is only way to put 3 people around a circular table.
So what’s the formula that can actually work in all the situations?

It depends on the context - see http://www.stat.ualberta.ca/people/schmu/preprints/ambiguity.pdf. Basically it depends on whether you care about isomorphic configurations or not.

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Never heard of it, but thank you! :blush: