Question

A company hired 15 new employees. They want to randomly assign 4 of them to work in the graveyard shift. In how many ways can this assignment be made

Answer 1

Answer:

This assignment can be made in 1365 ways.

Step-by-step explanation:

The order in which the shifts are assigned is not important. For example, employees A, B, C, D and D,C,B,A being assigned is the same thing. So, we use the combinations formula to solve this question.

Combinations Formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Assignment of 4 employees, from a set of 15. So

$C_{15,4} = \frac{15!}{4!(15-4)!} = 1365$