Chapter 0, Problem 27PR

To determine

whether each situation involves a permutation or a combination and then find the number of possibilities.

Answer to Problem 27PR

The numbers of ways are 455 ways .

Explanation of Solution

Given information :

Event is given as selecting 3 of 15 flavors of juice at the grocery store.

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

The number of ways is given by,

  $\begin{array}{c}C{}_3=\frac{15!}{3!12!}\\ =\frac{15\times 14\times 13\times 12!}{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\times 3\times 2}ways\\ =\frac{15\times 14\times 13}{3\times 2\times 1}ways\\ =5\times 7\times 13ways\\ =455ways\end{array}$

So, the numbers of ways are 455 ways .