Answer
There are C(20, 5) = 15504 ways to select 5 extras out of a group of 20 people
Step-by-step explanation
A combination is a grouping of outcomes in which the order does not matter (A and then B is the same pair as B and then A).
The number of combinations of n things chosen k at a time is found using:
[tex]C(n,k)=\frac{n!}{k!(n-k)!}[/tex]
In this case, the director has to select k = 5 extras out of a group of n = 20 people, that is,
[tex]C(20,5)=\frac{20!}{5!(20-5)!}=\frac{20!}{5!15!}=\frac{20\cdot19\cdot18\operatorname{\cdot}17\operatorname{\cdot}16\operatorname{\cdot}15!}{120\cdot15!}=\frac{20\cdot19\cdot18\operatorname{\cdot}17\operatorname{\cdot}16}{120}=15504[/tex]
