Question

How many ways can you divide 9 children into a team of 4, a team of 3, and a team of 2?

Answer 1

1260 ways

Explanation:

We want to arrange n people into x roles.

`m_(0)` is the number of people for the first role.

`m_(1)` is the number of people for the second role.

`m_(x)` is the number of people for the xth role.

The total number of arrangents is:

`T = (n!)/(m_(0)!m_(1)!...m_(x)!)`

In this question:

9 people

Team of 4

Team of 3

Team of 2

How many ways:

`T = (9!)/(4!3!2!) = 1260`