Question

In how many ways can 4 married couples attending a concert be seated in a row of 8 seats if: a) There are no restrictions? b) Each married couple is seated together?

Answer 1

a) 40,320

b) 384

Explanation:

Given,

The total number of seats = 8,

Also, these 8 seats are occupied by 4 married couples or 8 people,

a) Thus, if there is no restrictions of seating ( that is any person can seat with any person ),

Then, the total number of arrangement = 8 ! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320,

b) if each married couple is seated together,

Then, the 4 couples can seat in 4 pair of seats,

Also, in a pair of seats a couple can choose any of the two seats,

So, the total number of arrangement

`=4! * 2^4`

`=24* 16`

`=384`