Question

three couples go to the movies and sit together in a row of six seats. In how many ways can these people arrange themselves if each couple sits together?

Answer 1

3C2 = 3*2/ 2*1 = 3 if the couples themselves do not interchange
6 if they do interchange

Answer 2

i got tht too, but the book says it should be 48

Answer 3

If you treated each couple as one item, then you would have 3 choices for the first 2 seats, 2 for the next set, 1 for the last, or 3! permutations.
However, each couple can switch order. so if only the first couple swapped, we would get another 3!. ditto for the second and third couples, so in total
2^3 x 3! = 8*6 = 48