Chapter 0.4, Problem 14E

To determine

To find:The number of ways a band can choose the new singers.

Answer to Problem 14E

The band can choose the new singers in 816 ways.

Explanation of Solution

Given information:A band is choosing 3 new backup singers from a group of 18 who try out.

Calculation:Since the order in which the singers are chosen is not important, this situation involves combinations.

  $\begin{array}{l}C{}_3\\ =\frac{18!}{(18-3)!3!}\\ =\frac{18!}{15!3!}\\ =816\end{array}$

Thus, the band can choose the new singers in 816 ways.