9.10 In how many ways can three duty officers be selected from a group of 20 people?
9.10 The desired number of ways is equal to the number of combinations (without repetition) that can be formed from 20 elements taken three at a time. According to formula (9.4), we get

$C_{20}^{3}=\frac{20!}{17!3!}=\frac{20 \cdot 19 \cdot 18}{6}=1140$.

Answer: 1140 ways.