Question

In how many ways 8 persons can be seated on a round table such that two particular persons sit together

Answer 1

Given data:

8 persons can be arranged around a circular table where two persons among them insisted to sit together.

To find:

The number of ways in which we can arrange them around the circular table.

Step-by-step solution:

We can arrange the elements in a circular fashion in (n-1)! ways, where n refers to the number of elements to be arranged.

But, here 2 people among the 8 insisted to sit together.

So, by considering them as a single unit, we have to arrange 6+1 units = 7 units totally.

We can arrange those seven units in (7-1)! ways = 6! ways = 720 ways.

However, we can arrange the two people whom we consider as a single unit in linear fashion, in 2! ways = 2 x 1 = 2 ways.

So, we can arrange the 8 persons around a circular table with 2 of the 8 always sits together in 720 x 2 ways

                                             = 1440 ways.

Therefore, 8 persons can be arranged around a circular table (if two  persons always sit together) in 1440 ways.

Learn more:

In how many ways can 8 persons be seated at a round table

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