You can fit 6 people around a table...but look at it this way.
Lets say you have people, numbered 1, 2, 3, 4, 5, and 6. A random order could have them arranged like this...
3, 2, 5, 6, 1, 4
Because the table is circular, that would be the same as the following order...
6, 1, 4, 3, 2, 5
Can you see that? Im not sure if this is clear at all. You can look at it on a smaller scale. Take a table of 3 people, and look at the total number of combinations...
1) 1, 2, 3
2) 1, 3, 2
3) 2, 1, 3
4) 2, 3, 1
5) 3, 1, 2
6) 3, 2, 1
Now, since the table is circular, you will notice that there are repeating patterns. #1, #4, and #5 are the same. #2, #3, and #6 are the same. Therefore, there are really 2 combinations that are different = 2!.
