Question

Five carpenters, two baristas, and a sailor are to be seated around a circular table. How many different arrangements are possible if the carpenters 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.)

Answer 1

480 arrangements

Explanation:

Let's consider the carpenters 1 unit and the baristas 1 unit. Since rotations are equivalent, we can fix the position of the sailor at the front of the table. Then, the unit of carpenters can either be to the left or right of the sailor. This gives a total of 2 possible arrangements. For each of these two arrangements, we can have 5! * 2! = 240 ways to arrange the carpenters and baristas of each unit. This gives 240*2 = 480 different arrangements.