There are six chairs at a round table. A seating arrangement will be considered the same if everyone at the table has the same neighbor to the left and to the right.
a) How many different ways can we seat six people, assuming that one person sits in each chair?
b) How many different ways can we seat four people, assuming that two chairs are left empty?
c) How many different wats can we seat three couples if every person is seated next to their date?
a) is pretty obvious, which is 5!. However I'm not quite sure how to approach b and c. Any ideas? Thanks