A town employs 15 police officers. On a typical day, 8 of the officers are in patrol cars, 5 are foot patrol, and 2 are at the station. How many different job configurations are there?

Question

The town of Carson employs 15 police officers. On a typical day, 8 of the officers are to be assigned to duty in patrol cars, 5 are assigned to the foot patrol, and the remaining 2 are assigned to duty at the station. How many different job configurations are there?

Answer 1

Select 8 officers to be assigned to duty in patrol cars: C(15,8). There are 7 officers remaining.

Then select 5, who are assigned to the foot patrol. C(7,5) The remaining 2 will stay in the office.

C(15,8)*C(7,5)*C(2,2) = 135,135