Hello, billym!

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.