5. In how many different ways can 30 workers be divided into 3 teams of 10 people each?
5. 10 workers, forming the first brigade, can be chosen from thirty in $C_{30}^{10}=\frac{30 \cdot 29 \cdot \ldots \cdot 21}{10!}$ ways. After this, from the remaining 20 workers, 10 workers for the second brigade can be chosen in $C_{20}^{10}=\frac{20 \cdot 19 \cdots 11}{10!}$ ways. By combining each way of forming the first brigade with each way of forming the second brigade, we get a total of $\frac{30 \cdot 29 \cdot \ldots \cdot 11}{(10!)^{2}}=\frac{30!}{(10!)^{3}}$ ways to distribute the workers into three brigades. However, here the distributions that differ only by the numbering of the brigades are counted as different; therefore, the obtained number must be divided by $3!$ — the number of ways to assign three numbers to three brigades. Thus, the desired number of ways is

$$
\frac{30!}{3!(10!)^{3}}=2775498395670
$$

Note. Similarly, it can be concluded that from $n k$ workers, $k$ brigades of $n$ workers each can be formed in $\frac{(n k)!}{(n!)^{k} k!}$ ways.