SOLUTION: In how many ways can an event organizer seat nine guests around a table?

Question 1190640: In how many ways can an event organizer seat nine guests around a table?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
There is a relationship between the linear arrangements and circular arrangements. In fact linear arrangements of different objects is equal to circular arrangement of these objects .
In how many ways can an event organizer seat nine guests around a table?
In a circular arrangement we first have to fix the position for the first guest , which can be performed in only one way (since every position is considered same if no one is already sitting on any of the seats), also, because there are no mark on positions.
Now, we can also assume that remaining guests are to be seated in a line, because there is a fixed starting and ending point i.e. to the left or right of the first guest.
Once we have fixed the position for the first guest we can now arrange the remaining guests in ways.
Therefore here we have, no. of circular arrangements of 9 guests is
ways

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