Six people sit around a circular table.
Person A and B must not sit next to each other.
How many ways are there of seating them?
With 6 people around a circular table,
. . there are: . ways to seat them.
Duct-tape and together
. . Then we have 5 "people" to arrange: .
There are: . ways to seat them.
But the 5 "people" could be: .
Hence, there are: . ways that and are adjacent.
Therefore, there are: . ways in which and are not adjacent.