Example 5a Sheldon Ross on Combinatorics

A police department in a small city consists of 10 officers. If the department policy is to have 5 of the officers patrolling the streets, 2 of the officers working full time at the station, and 3 of the officers on reserve at the station, how many different divisions of the 10 officers into the 3 groups are possible?


There are  \(10 ! \over 5! 2! 3 ! \) possible divisions.