A hint to get started
Seat ten people with two couples
A group of ten people consists of four single women, two single men and 2 couples. The ten people are seated randomly in a circle. Find the number of arrangements if (i) there is no restriction, (ii) the couples must seat together, (iii) the seats are of different colours.
CJC · Lecture · Self-Practice 6
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.