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  • A group of 8 friends is seated at a round table. How many different seating arrangements are possible if two particular friends must be seated next to each other?  <div

A group of 8 friends is seated at a round table. How many different seating arrangements are possible if two particular friends must be seated next to each other?

 

Option: 1

1440


Option: 2

720


Option: 3

1340


Option: 4

740


Answers (1)

best_answer

To solve this problem, we can treat the pair of friends who must be seated next to each other as a single entity. Let's call this pair AB. Now we have 7 entities (AB, C, D, E, F, G, H) to arrange around the table.

We can arrange these 7 entities in a circle which is given by,

\begin{aligned} &(7-1) !=6 !\\ &6 !=720 \end{aligned}

Within the pair AB, the two friends can be arranged in 2! = 2 different ways (AB or BA).

Therefore, the total number of seating arrangements where the two particular friends are seated next to each other is,

720 \times 2=1440

Hence, there are 1440 different seating arrangements of the 8 friends at the round table where the two particular friends are seated next to each other.

 

Posted by

Devendra Khairwa

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