9.22 Thirty people are divided into three groups (I, II, and III) with 10 people in each. How many different group compositions are possible?
9.22 Group I of 10 people can be formed in $C_{30}^{10}$ ways. From the remaining 20 people, Group II can be formed in $C_{20}^{10}$ ways, and each time the remaining 10 people automatically form Group III. Since each selection of Group I is paired with each selection of Group II, the total number of group compositions is:

$$
C_{30}^{10} \cdot C_{20}^{10} \cdot C_{10}^{10}=\frac{30!}{20!10!} \cdot \frac{20!}{10!10!}=\frac{30!}{(10!)^{3}}
$$

answer: $\frac{30!}{(10!)^{3}}$ ways.