In how many ways can 8 people be seated at a circular table if two particular people must sit next to each other?
Given that,
There are 8 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 7 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,
There are 6! 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.
So there are 1440 ways to seat the 8 people at the circular table if the two particular people must sit next to each other.
Therefore, the number of ways to arrange the people in a circular table is 1440.
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