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

This assignment can be made in 1365 ways.

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) = (n!)/(x!(n-x)!)`

In this question:

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

`C_(15,4) = (15!)/(4!(15-4)!) = 1365`