Ex: 6 persons, Amal, Bimal, Chand, Diana, Emily and Farah are to be seated at a round dinner table. Amal and Diana are to sit next to each other. In how many ways can you allot seats for them ?
We first consider Amal and Diana as one person. Five persons can be seated in 5! ways. Since the positions of Amal and Diana can be interchanged, we multiply this number by two and get 2 x 5!. However, the whole group can be rotated as: AD-B-C-E-F F-AD-B-C-E E-F-AD-B-C etc. which do not give new arrangements. So we divide the number by 5 and get 2 x 5! 5 = 48