Question

In how many ways can 12 party guests be seated around a circular table? What if two people want to sit directly next to each other?

Answer 1

If 12 persons are arranged in a linear way, there are 12! ways to do so. But when it come to a circular arrangement, total number of arrangements = 12!/12=11!.=39976800

If two people want to sit directly next to each other then we consider they are one unit, therefore 11 units are arranged in a circular table.Therfore total arrangement is= 10!*2

Here multiple 2 due to the two people want to sit directly next to each other can interchange between them.

Therefore after sitting two people directly next to each other

Then number of arrangements is=10!*2=7257600.

Its probability is= 0.18154.