Thread: easy, easy question

Can somebody please help me out with this? I had the answer easily the first time, but now my mind is blank:

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?

Hello, billym!

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?

For reference, let the couples be: .


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.

Originally Posted by Soroban

Hello, billym!

For reference, let the couples be: . B,b),\C,c),\D,d),\E,e)" alt="(A,a),\B,b),\C,c),\D,d),\E,e)" />


Duct-tape the couples together.

I've always suspected you had an evil streak, Soroban!

I have a friend who swears you can do anything with duct-tape. Now I know you can even solve math problems with it!

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.

Hello, HallsofIvy!

I have a friend who swears you can do anything with duct tape.

Duct tape is like The Force.

It has a light side and dark side
and it holds the universe together.