How many different seating orders are there for eight people sitting in a circle?
Question
How many different seating orders are there for eight people sitting in a circle?
Solution
When arranging people in a circle, one way to think about it is to fix one person's position and then arrange the remaining people. This is because in a circular arrangement, there is no distinct "first" position, so all arrangements are considered rotations of each other.
So, if we fix one person's position, we are left with 7 people to arrange.
The number of ways to arrange n distinct items is given by the formula n!, which stands for n factorial, and is calculated as n*(n-1)(n-2)...32*1.
So, the number of ways to arrange the 7 remaining people is 7!, which is 7654321 = 5,040.
Therefore, there are 5,040 different seating orders for eight people sitting in a circle.
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