Question

6 friends (Andy, Bandy, Candy, Dandy, Endy and Fandy) are out to dinner. They will be seated in a circular table (with 6 seats). Andy and Bandy want to sit next to each other to talk about the Addition Principle, Bandy and Candy want to sit next to each other to talk about the Principle of Inclusion and Exclusion. How many ways are there to seat them?

Answer 1

A,B,C must seat together. So they can be taken as one unit with internal permutation of 3!
There are four different units, around a circle, so total ways=\(\frac{4! \times 3!}{4}\)