The owner of a stereo store wants to advertise that he has many different sound systems in stock. The store carries 7 different CD players, 8 different receivers and 10 different speakers. How many different sound systems can the owner advertise?
The owner can advertise a total of 560 different sound systems!
The way to think about this is that each combination looks like this:
1 Speaker (system), 1 Receiver, 1 CD Player
If we only had 1 option for speakers and CD players, but we still have 8 different receivers, then there would be 8 combinations. If we only fixed the speakers (pretend that there is only one speaker system available), then we can work down from there:
I'm not going to write every combination, but the point is that even if the number of speakers is fixed, there would be:
different combinations! Now, we'll add ANOTHER layer of complexity by considering the options for speakers: