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?

Accepted Solution

Answer:a) 40,320b) 384Step-by-step 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[tex]=4! \times 2^4[/tex][tex]=24\times 16[/tex][tex]=384[/tex]