Answer:
There are 35 different ways that three new heads be appointed.
Step-by-step explanation:
The order of the manager are not important. For example, John, Elisa and Rose is the same outcome as Elisa, John and Rose. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Head of 3 managers from a set of 7. So
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
[tex]C_{7,3} = \frac{7!}{4!(3)!} = 35[/tex]
There are 35 different ways that three new heads be appointed.
