Calculating the Number of Possible Entertainment System Configurations
When setting up an entertainment system, customers often have the flexibility to choose from a variety of components to create their desired configuration. In this article, we will explore how to determine the number of possible system configurations when a customer can select one item from each of the following categories: amplifiers, compact disc (CD) players, and speaker models.
Amplifier Selection
Let's assume that the customer can choose from 4 different amplifier models. This means the customer has 4 options for the amplifier component of the entertainment system.
CD Player Selection
In addition to the amplifier, the customer can also select a CD player. In this case, the customer has 6 different CD player models to choose from.
Speaker Selection
Finally, the customer can select one of 5 different speaker models to complete the entertainment system.
Calculating the Total Number of Configurations
To determine the total number of possible system configurations, we need to multiply the number of options for each component. This is because the customer can independently choose one item from each category.
The total number of possible configurations is calculated as follows:
- Number of amplifier options: 4
- Number of CD player options: 6
- Number of speaker options: 5
Total number of configurations = 4 (amplifiers) × 6 (CD players) × 5 (speakers) = 120 possible configurations
Therefore, the customer has 120 different ways to configure the entertainment system by selecting one amplifier, one CD player, and one speaker model.
This calculation is based on the principle of multiplication in combinatorics. Since the customer can choose each component independently, the total number of possible configurations is the product of the number of options for each component.
By understanding this concept, customers can explore the various combinations of components to find the entertainment system that best suits their needs and preferences.