Question

Suppose you are managing 15 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 taht the number of employees on each project are as follows: 9, 4, 2

Answer 1

There are 17,418,240 different ways to choose the teams.

Explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

`A_(n) = n!`

In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 9, 4, 2?

This is:

Arrangement of 9 elements, followed by an arrangement of 4 elements followed by an arrangement of 2 elements. So

`T = A_(9)*A_(4)*A_(2) = 9!*4!*2! = 362880*24*2 = 17418240`

There are 17,418,240 different ways to choose the teams.