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  • If two specific individuals must sit next to one another, how many different ways are there to seat 12  guests at a round table?  Option: 1</

If two specific individuals must sit next to one another, how many different ways are there to seat 12  guests at a round table?

 

Option: 1

5257500


Option: 2

3456200


Option: 3

6321470


Option: 4

7257600


Answers (1)

best_answer

Given that,

There are 12 people seated at a circular table.

If two particular people must sit next to each other at a circular table, we can treat them as a single unit. This means that we have 11 units to arrange around the table, with one of the units being the pair of people who must sit next to each other.

The number of ways to arrange n distinct objects in a circle is (n-1)!.

Thus

(11-1) !=10 \text { ! }

There are 10! ways to seat the people around the circular table.

However, we need to account for the fact that the two particular people in the pair can sit next to each other in two different ways (either person A can sit to the left of person B, or person A can sit to the right of person B). 

So we need to multiply the number of arrangements we got earlier by 2 to account for this.

Therefore, the total number of ways to seat the 8 people at the circular table, with the two particular people sitting next to each other, is:

\begin{aligned} & 2 \times 10 !=2 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \\ & 2 \times 10 !=7257600 \end{aligned}

Therefore, the number of ways to arrange the people in a circular table is 7257600.

 

 

Posted by

Gaurav

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