Question

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.

Receiver: Kenwood, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules to answer the following questions.
(a) In how many ways can one component of each tybe be selected? _____

Answer 1

Using the product rule, the total number of ways a customer can select one component of each type for their stereo system from the given options is 96 different combinations.

Step-by-step explanation:

The question requires the use of the product rule in combinatorics, which is a principle in mathematics that states when there are multiple independent events or choices, the total number of combined outcomes is the product of the number of choices for each event or component. To find out in how many ways one component of each type can be selected, we multiply the number of options for each component:

• Receiver: 3 choices (Kenwood, Sony, Sherwood)
• Compact disc player: 4 choices (Onkyo, Pioneer, Sony, Technics)
• Speakers: 2 choices (Boston, Infinity)
• Turntable: 4 choices (Onkyo, Sony, Teac, Technics)

Using the product rule, the total number of ways one component of each type can be selected is calculated as follows:

3 receivers × 4 compact disc players × 2 speakers × 4 turntables = 96 different combinations.

Therefore, there are 96 different ways a customer can select one component of each type for their stereo system.