Question

In how many ways can three couples be seated in a row so that each couple sits stogether (namely next to each other): • in a row, 48 48 • in a circle? ? Hint (1 of 1): As in the general comment, recall that rotations matter. It may be useful to imagine a round table with 6 chairs, and a single mark on the table, between two specific chairs. Observe that for some configurations of the 6 people, the mark is between two different couples, denoting the mark by *, e.g. * A, A1 CC2B2B, where A, B, and C represent the different couples, and the because of the circular arrangment Bi seats next to the *. For other configurations, the mark separates two members of the same couple for example * ACC2B2B1A2, where A2 seats next to the *. You can count the number of configurations of each type.

Answer 1

- No. of ways for three couples be seated in a row such that each carple sits together will be = (3!).(9116211 (21) = 48 - Husband wife ear be left on Permutation of couples right in two . We o wq wz M3 Leta first we selt 3 males in a cerele, hoof ways of such dargement wiom, = 21 =g Now a wife of each husband cat sitt either left of her husband or right of her husband die. 21 permutation Hawa tatal possible way for all there couples to sitt in a cascle so that couple is together will be = 2 ( 211 (9!) (217) - 2+ = [16].