Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.

Let the married couples by a1,a2,a3.
Then the number of ways in which spouses can seat next to each other is 3!=6.
As each couple can be seated in 2! ways.
So, total number of ways so tha spouses sit next to each other =3!2!2!2!
=48

And if three ladies sit together, then three must also sit together.
Hence, ladies and men can be arranged altogether among themselves in 3! ways.
So, total number of ways so tha spouses sit next to each other =4!3!1!
=144

Final Answer
Number of ways in which spouses sit next to each other is 48.
Number of ways in which ladies sit next to each other is 144.