How many unique ways are there to arrange 5 people around a circular table?

[jgens]

Homework Statement

How many unique ways are there to arrange 5 people around a circular table?

Homework Equations

N/A

The Attempt at a Solution

This should be a pretty simple question, but I can't seem to focus on much of anything now, so I'm really not confident in my solution. I figured that if it were a straight line or something like that, then there would be 5! unique ways of arranging the people. However, since this is a round table, I guessed that ways of arranging individuals which were merely a rotation from another orientation shouldn't be counted more than once. Since there were five corners per se, I figured that only 1/5 of the original 5! ways of arranging people were actually unique; and thus, there would be 4! unique ways of arranging 5 people around a circular table.

I know that this reasoning isn't rigorous by any stretch of the imagination, but I was wondering if it is even correct (or if the answer is close to correct). Thanks for any feedback.

 

[Willian93]

think about how 5 people sit in a row. in circular shape, we can't exactly know the start point. So we Freeze one person and all other 4 people rotates, so you are actually in a right directions

 

[HallsofIvy]

Yes, you can seat one person anywhere on the table, leaving the other 4 to be seated as if that person were one end of a straight table. 4! is the correct ansswer.