Chapter 0.5, Problem 11E

To determine

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

Answer to Problem 11E

The numbers of possibilities are 715.

Explanation of Solution

Given information :

It is given that to select 4 of 13 different colored balloons.

In the given event, the order of the colored balloons does not matter; therefore, it is a combination.

The number of possibilities is given by,

  $\begin{array}{c}C{}_4=\frac{13!}{4!\left(13-4\right)!}\\ =\frac{13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\\ =715possibilities\end{array}$

So, the numbers of possibilities are 715.