In how many ways 8 persons can be arranged around a circular table if two
persons always sit together.
Answers
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.
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