Chapter 8.5, Problem 13E

To determine

To find: the number of possible system configurations.

Answer to Problem 13E

Number of possible system is 120.

Explanation of Solution

Given information:

A customer can choose one of four amplifiers, one of ten stereo receivers, and one of five speaker models for an entertainment system.

Calculation:

One of four amplifier mean:

  $\begin{array}{c}{}_4{C}_1=\frac{4!}{\left(4-1\right)!1!}\\ =\frac{4\times 3\times 2\times 1}{3\times 2\times 1\times 1}\\ =4\end{array}$

One of six compact disc players mean:

  $\begin{array}{c}{}_6{C}_1=\frac{6!}{\left(6-1\right)!1!}\\ =\frac{6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1\times 1}\\ =6\end{array}$

One of five speaker medels mean:

  $\begin{array}{c}{}_5{C}_1=\frac{5!}{\left(5-1\right)!1!}\\ =\frac{5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 1}\\ =5\end{array}$

Numbers of possible system for an entertainment system is,

  $\begin{array}{c}{}_4{C}_1{\times }_6{C}_1{\times }_5{C}_1=4\times 6\times 5\\ =120\end{array}$

Hence number of possible system is 120.