I have to count these for class
There are 18 padded chairs around a circular table, and the chairs are numbered from 1 through 18 . How many ways can five people take their seats, so that no two people are adjacent?
n=18;r=5;k=1; a=n * (n - (r*k) - 1) nPr (r - 1)
Where k stands for minmum chair separation between any 2 persons
and k<=[n - r] / r and n=number of chairs, r=number of people to be seated
and k=1 or number of chairs 2 people must be separated by.
Answer: 213,840 ways.