If n different people are sitting around a table, the possibility of 2 persons sitting next to each other is 2/(n-1).
1) Total possible arrangement of n people on a table = n! / n = (n-1)! 2) Total possible arrangement of n-1 people (assuming those two sitting together would be treated as a single person) = 2* (n-1)! / (n-1) = 2* (n-2)! There is a 2 in the equation because the two persons are not identical.
The possibility of 2 persons sitting next to each other = 2* (n-2)! / (n-1)! = 2/(n-1)