## Precalculus (6th Edition) Blitzer

We know that the order in which the four actors are selected does not make a difference as the designation for all the four actors would be the same. The ordered arrangement in which the order of the arrangement does not make a difference is solved using the concepts of combinations. The four actors are to be selected from a group of twenty actors. So, $n=20,r=4$. Hence, \begin{align} & _{20}{{C}_{4}}=\frac{20!}{4!\left( 20-4 \right)!} \\ & =\frac{20!}{4!16!} \\ & =\frac{20\times 19\times 18\times 17\times 16!}{24\times 16!} \\ & =4845 \end{align}