# Three couples have reserved seats for a Broadway musical. How many different ways they can sit if two members of each couple wish to sit together?

Mar 20, 2016

If the seats all face the stage and are not in some kind of circle:

2^3 xx 3! = 48

#### Explanation:

Assuming the seats are all facing the stage and not in some kind of circle, then there are three designated pairs of seats.

The three couples can be assigned to these three pairs of seats in 3! = 6 ways.

Then independently, each couple can be seated within their pair of seats in $2$ possible ways, giving a factor of ${2}^{3} = 8$.

So the total number of ways that the couples can be seated is:

2^3 * 3! = 8 * 6 = 48