Three married couple are to be seated in a row having six seats in a c

1.	Three married couple 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 ladies sit together.
Answer» (i) Three couples can be seated in a row in ³P₃ = 3! Ways. Now, in each couple, the spouses can be arranged in ²P₂ = 2! , ways Thus for three couples, number of arrangements = 2! × 2! × 2! ∴ Total number of ways in which spouses are seated next to each other = 3! × 2! × 2! × 2! = 6 × 2 × 2 × 2 = 48 ways. (ii) Now, if the three ladies are to be seated together, there are regard 3 ladies as one block. Therefore, there are now 4 people can be arranged in ⁴P₄ = 4! = 24 ways. But 3 ladies can interchange their position in 3! = 6 ways ∴ Total number of arrangements in which 3 ladies sit together = 24 × 6 = 144.

Three married couple 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 ladies sit together.

Answer»

(i) Three couples can be seated in a row in ³P₃ = 3! Ways.

Now, in each couple, the spouses can be arranged in ²P₂ = 2! , ways

Thus for three couples, number of arrangements = 2! × 2! × 2!

∴ Total number of ways in which spouses are seated next to each other = 3! × 2! × 2! × 2! = 6 × 2 × 2 × 2 = 48 ways.

(ii) Now, if the three ladies are to be seated together, there are regard 3 ladies as one block.

Therefore, there are now 4 people can be arranged in ⁴P₄ = 4! = 24 ways.

But 3 ladies can interchange their position in 3! = 6 ways

∴ Total number of arrangements in which 3 ladies sit together = 24 × 6 = 144.