Chapter 11, Problem 1T

A person can purchase a particular model of a new car with a choice of ten colors, with or without automatic transmission, with or without four-wheel drive, with or without air conditioning, and with two, three, or four radio-CD speakers. How many different options are there for this model of the car?

To determine

To calculate: The number of ways to purchase a car when choices given in colors are10, choices in AC are 2, choices in four-wheel drive as well as choices in the automatic transmission are 2, and the choices in CD player are3..

Answer to Problem 1T

Solution:

The number of ways to purchase a car is $240$.

Explanation of Solution

Given:

The choices given in colors are 10, choices in AC are 2, choices in four-wheel drive as well as choices in the automatic transmission are 2, and the choices in CD player are 3.

Calculation:

The number of ways to purchase a car can be calculated by multiplying the given number of choices in color to the given number of the choices in AC, the choices in automatic transmission, choices in four-wheel drive, and the choices in CD player.

Compute the number of ways to purchase a car using the equation as shown below:

$\begin{array}{c}\text{No}\text{. of ways to purchase a car}=\text{Choice in color}\times \text{Choice in AC}\times \text{Choice in drive}\\ \times \text{Choice in automatic transmission}\times \text{Choice in CD player}\\ =10\times 2\times 2\times 2\times 3\\ =240\end{array}$