## Task B-4.4.

In a mathematics team competition, 5 teams participate. Each team consists of 3 students, including the team leader. All 5 teams sit at the same round table, so that students from the same team sit together, one next to the other, and the team leader is always between the members of their team. How many different seating arrangements are there around the round table? (Arrangements are considered the same if one can be obtained from the other by rotation. Arrangements are different if there is a pair of people who sit one to the left of the other in one arrangement, but not in the other.)
## Solution.

Since the team leaders determine where the rest of the team members will sit, and there are 5 such leaders, and it is a round table, the number of possible arrangements is $(5-1)!=4!=24$.

After arranging the team leaders, the rest can be seated in 2 ways around each leader. Since there are 5 different teams, the total number of arrangements is: $2^{5}=32$.