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 us denote married couples by S₁, S₂, S₃, where each couple is considered to be a single unit as shown in the

Following figure:

Then the number of ways in which spouces can be seated next to each other is 3! = 6 ways.

Again each couple can be seated in 2! Ways. Thus the total number of seating arrangement so that spouces it next to each other = 3! × 2! × 2! × 2! = 48

Again, if three ladies sit together, then necessarily three men must sit together. Thus, ladies and men can be arranged altogether among themselves in 2! Ways. Therefore, the total number of ways where ladies sit together is 3! × 3! × 2! = 144