Permutation Problem need help So there is 7 people seated at a  circular table. Person A cant move. How many ways can they be seated  If person A stays in their seat?
 A: I find these types of permutations fascinating. It may be helpful to draw a diagram to get an idea of what's going on. The image below is courtesy of Wolfram Alpha: 
Here, we have four people sitting in a circle. In this diagram, they show person 1 in a fixed position. Intuitively, you can see that there are $3!$ possible permutations. The general formula for circular permutations is $(n-1)!$, which can be proved via induction.
There is another way to think about it, which I prefer since I find it more intuitive. In your case, you have 7 people sitting in a circle. How many ways can they be arranged? If they were in a linear pattern, then there would be $7!$ ways. However, when they are in a circle, this isn't the case. Imagine if you put them in a particular order, say $1,2,3,4,5,6,7$. Now rotate them by one: now you have $7,1,2,3,4,5,6$. But they're still in the same order since they're in a circle! $7$ is still between $1$ and $6$. After seven rotations, they'll be where they started. Hence, you have $7!/7 = 6!$ possible permutations. So the general idea is to calculate the number of linear permutations, then divide it by the number of people in the circle. Hope that helps!
A: In general circular permutations are evaluated by (n-1)! so you have 6!
