2, 6, $(n-1)!$
Work Step by Step
As the people will form a circle, we can fix one position and think the problem as arranging the rest $n-1$ members. The next seat after fixing the first one has $n-1$ choices, and the next one $n-2$ choices and so on. So the total number of ways is: $(n-1)!$ For example, n=3, #ways = 2; n=4, #ways=6, etc.