Originally Posted by
Plato Once we have established the “head of table”, the table is now ordered. All we need to do is count the number of ways to seat the other nine. That is (9!) ways without any other restrictions. However, there are other restrictions. So lets count the cases we don’t want. There are 2(8!) ways for Nancy and Henry are seated together. The same for Henry and Wilson to be seated together. But if we add those two we have counted the cases where Nancy, Henry, and Wilson are seated as a threesome with Henery between them: 2(7!).
Remove the ones we don’t want from the total:
(9!)-[2(8!)+2(8!)-2(7!)].