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?
Assumig peope are the same an rotations are the same
tie each person in a chair to a chair on the right,
so now there are 5 double people and 8 other seats that is 13 altogether
Pur one double in place, down't matter where, that takes care of rotations
now there are 12C4 = 495 ways