A hint to get started
Seat eight distinct people round a table
In how many ways can 4 boys and 4 girls be seated at a round table if (i) there is no restriction, (ii) the boys and the girls must be separated, (iii) one particular girl must be seated between 2 particular boys?
CJC · Lecture · Example 18
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.