Question

You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 9 different TVs, 15 types of surround sound systems, and 24 types of DVD players. How many different home theater systems can you build?

Answer 1

You can build 3,240 different home theater systems.

Explanation:

The possible combinations can be calculated multypling the number of TVs available, the number of sorround systems available and the amount of DVD players avalaible.

`C=X_(tv)\cdot X_(ss)\cdot X_(dvd)=9\cdot15\cdot24=3240`

This is because for each type of TV, we can combine it with any type of sorruond system. This makes 15 combinations for each TV type. If we have 9 TV types, we have 9*15=135 combinations. Each of these combinations can be completed with one of the 24 types of DVD player, so we have 135*24=3240.