Answer:
The assignment can be made in 630,630 ways.
Step-by-step explanation:
Arrangement formula:
We want to arrange n people into x roles.
[tex]m_{0}[/tex] is the number of people for the first role.
[tex]m_{1}[/tex] is the number of people for the second role.
[tex]m_{x}[/tex] is the number of people for the xth role.
The total number of arrangents is:
[tex]T = \frac{n!}{m_{0}!m_{1}!...m_{x}!}[/tex]
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?
[tex]T = \frac{15!}{6!4!5!} = 630630[/tex]
The assignment can be made in 630,630 ways.
