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Question
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.
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Solution
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 sit 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!
= 6 × 6 × 2
= 72
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