Kenneth Rosen Edition 7 Exercise 6.1 Question 45 (Page No. 397)

Question

How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?

Comments

In the above image see the two seatings, in both the seatings everyone have same neighbour.

So when calculating the permutations consider them as same and not different.

Answer 1

total no of ways six people around a circle table is 5!+120

but if left right neighbor of a people  is same as right left neighbor  for all 6 people then they we be consider as same  means no we get should be divided by 2   (see the image in comment  by sakharam )

so answer is 120/2=60