Question

You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 22 different TVs, 6 types of surround sound systems, and 22 types of DVD players. How many different home theater systems can you build?

Answer 1

According to the given question, I can choose from 22 different TVs, 6 types of surround sound systems, and 22 types of DVD players.

Therefore from 22 different TVs I can select at $22$ ways of TVs ,

from 6 types of surround sound systems I can select at $6$ ways of surround sound systems, and

from 22 types of DVD players I can be select at $22$ ways of DVD players.

Therefore, number of different home theater systems can I build is

$=\left (22\times 6\times 22 \right )$ ways

$=2,904$ ways.