Suppose you are managing 17 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the same probability of getting choosen. In how many different ways can the teams be chosen so that the number of employees on each project are as follows:8,3,3

24414 combinations

Step-by-step explanation:

Solution:-

- We have 17 employees that needs to be managed for a project.

- We will choose all of our employees equally likely for 3 projects.

Project 1 = 8 spacings

- So we have 17 available employees to choose from. So we choose (combinations):

Project 1 = 17C8 = 24310 combinations

- We are left with 17 - 8 = 9 employees, for the next project:

Project 2 = 3 spacings

- So out of the available 9 employees project 2 would have:

Project 2 = 9C3 = 84 combinations

- We are left with 9 - 3 = 6 employees, for the next project:

Project 3 = 3 spacings

- So out of the available 6 employees project 3 would have:

Project 3 = 6C3 = 20 combinations

- The total number of combinations fro selecting 17 employees for each project would be:

24310 + 84 + 20 = 24414 combinations