How many ways are there to seat six people around a circular

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

Solution

we have given

seat six people around a circular table where two seatings are

considered the same when everyone has the same two neighbors without regard to

whether they are on the right or the left

First person or person-A will sit someplace

first person can sit anywhere

the other five person can sit these ways :

5(B sitting ways)*4(C sitting ways)*3(D sitting ways)*2(E sitting ways)*1(F sitting ways)

so, other can be arranged in 120 ways

the exact reverse of each other will give us \"the same\" seating,

so this number double counts them

So all that remains is \"to get rid of\" the overcounted arrangements by dividing out by two

Hence, the number of ways six people can seat = 120/2=60 ways...........Answer