In how many ways can we seat 6 people at a round table if John and Sam insist on sitting next to each other? (Two seatings are equivalent if one is a rotation of the other.)
there is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.
But John and sam are tied together so thet are the equaivalent of one person.
so that is only 4 people.
4! *2 because it could be john, sam or sam, john.
2*3*4*2 = 48 permutations.