Question 1164491: In how many ways 10 people can be arranged in a circle?
Answer by greenestamps(13208)   (Show Source):
You can put this solution on YOUR website!
10 people in a line can be arranged 10*9*8*...*2*1 = 10! ways.
Arranged around a circle, they can be arranged in only 10!/10 = 9! ways, because you don't know where the "starting point" is.
For a simpler case, consider three people, A, B, and C.
In a line, the three people can be arranged in 3! = 6 ways:
ABC ABC BAC BCA CAB CBA
But arranged in a circle, the arrangements ABC, BCA, and CAB are all the same, and the arrangements ACB, CBA, and BAC are all the same. So the number of arrangments around a circle for three people is 3!/3 = 2! = 2.
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