Five journalists, two baristas, and a sailor are to be seated around a circular table. How many different arrangements are possible if the journalists must all sit together (in five consecutive seats) and the baristas must sit next to each other? (Two seatings are considered equivalent if one seating can be obtained from rotating the other.)
First, we can seat the journalists. Then we seat the baristas, then the sailor. There are 5! ways to seat the journalists, then 2! ways to seat the baristas, then 1! way to seat the sailor. Then we divide by 8, so there are 5!*2!*1!/8 = 30 ways to seat everyone.