For reference, let the couples be: .How many ways are there to seat 10 people, consisting of 5 couples,
in a row of seats (10 seats wide) if all couples are to get adjacent seats?
Duct-tape the couples together.
We have 5 "people" to arrange: .
There are: . permutations.
But for each permutation, the couples can be "swtiched".
. . could be , could be , and so on.
There are: . possible switchings.
Therefore, there are: . seating arrangements.