SOLUTION: In how many ways can 5 people be seated around a circular table if two of them insist on sitting besides each other?

If we temporarily consider two people "A" and "B" as a unit, we have essentially four people to seat: { {AB}, C, D, E }



Four people can be seated at a circular table in 3! = 6 ways.



Now we must double it for {AB} and {BA} are two unique arrangements:



2*6 =  ways to seat five people such that two of them are always together.