SOLUTION: In how many ways can 8 persons be seated at a round table if a certain 2 are to sit next to each other?

At given context, those two persons who are to sit next to each other, represent one object with 2 states.


So, the problem is about circular permutations of 7 objects, where one fixed object can be in one of the two states.


The number of circular permutations then is   = 2*6! = 2*6*5*4*3*2*1 = 1440.    ANSWER


The factor  "2"  accounts for the order AB or BA of the two selected persons sitting next to each other.