Question

A company has hired 15 new employees, and must assign 6 to the day shift, 4 to the night shift, and 5 to the graveyard shift.

In how many ways can the assignment be made?

Answer 1

The assignment can be made in 630,630 ways.

Explanation:

Arrangement formula:

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:

15 employees

6 to the day shift.

4 to the night shift.

5 to the graveyard shift.

In how many ways can the assignment be made?

`T = (15!)/(6!4!5!) = 630630`

The assignment can be made in 630,630 ways.