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  • A group of 5 friends are going on a road trip and want to sit in a row of 6 seats in a van. How many different seating arrangements are possible if two friends refuse to sit next to each other?

A group of 5 friends are going on a road trip and want to sit in a row of 6 seats in a van. How many different seating arrangements are possible if two friends refuse to sit next to each other?

 

Option: 1

1200


Option: 2

13600


Option: 3

1440


Option: 4

1020


Answers (1)

best_answer

To find the number of different seating arrangements where two friends refuse to sit next to each other, we can use the concept of permutations with restrictions.

First, let's consider the two friends who refuse to sit next to each other as a single entity. We can arrange this entity and the remaining 3 friends in a row in (6 - 2 + 1) =5!  seats in ways.

Within this arrangement, the two friends who refuse to sit next to each other can be seated in two ways: either the first friend of the pair sits on the left or the right side of the entity. Therefore, the total number of seating arrangements for the two friends is 2.

Now, we need to consider the remaining 3 friends who can sit in the remaining 3 seats. This can be done in 3! ways.

Therefore, the total number of different seating arrangements where the two friends refuse to sit next to each other is 5!\times 2\times 3!

Calculating this expression:
5!\times 2\times 3!= 120\times 2\times 6= 1440.

So, there are 1440 different seating arrangements possible in the given scenario.

 

 

Posted by

Nehul

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