Chapter 0.5, Problem 20E

To determine

the ways can they choose the new singers.

Answer to Problem 20E

The numbers of possibilities are 816possibilities .

Explanation of Solution

Given information :

It is given that a band is choosing 3 new backup singers from a group of 18 who try out.

In the given event, arrangement does not matter so it is combination.

The number of possibilities is given by,

  $\begin{array}{c}C{}_3=\frac{18!}{15!\times 3!}\\ =\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2}{15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 3\times 2}possibilities\\ =\frac{18\times 17\times 16}{3\times 2}possibilities\\ =3\times 17\times 16possibilities\\ =816possibilities\end{array}$

So, the numbers of possibilities are 816possibilities .