Exercise 3.1.11. 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?
Exercise 3.1.12. In order to play a game of basketball, 10 children at a playground divide themselves into two teams of 5 each. How many different divisions are possible?
Answer (1)
There are 2520 different ways to divide 10 police officers into 3 groups, with specific roles for each group. For 10 children dividing into 2 basketball teams of 5, there are 126 unique divisions. Using combinations helps to easily calculate the divisions based on the specific group sizes and indistinguishable teams. ;
