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?

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slicergiza slicergiza · Answer 1 · 2019-07-02T14:27:43+02:00

Answer:

a) 40,320

b) 384

Step-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]