Example 3. In how many ways can three people be selected for three identical positions from ten candidates?
Solution. According to formula (1.3.4), we find

$$
C_{10}^{3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10!}{3!\cdot 7!}=\frac{10 \cdot 9 \cdot 8}{1 \cdot 2 \cdot 3}=120
$$