Question

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?

Answer 1

The owner can advertise a total of 560 different sound systems!

Explanation:

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:

`S, R_1, C_1`
`S, R_1, C_2`
`S, R_1, C_3`
...
`S, R_1, C_8`
`S, R_2, C_1`
...
`S, R_7, C_8`

I'm not going to write every combination, but the point is that even if the number of speakers is fixed, there would be:

`N_"Receiver"xxN_"CD Player"`

`7xx8=56`

different combinations! Now, we'll add ANOTHER layer of complexity by considering the options for speakers:

`C_"Total"=N_"Speaker"xxN_"Receiver"xxN_"CD Player"`

`C_"Total"=10xx7xx8`

`color(green)(C_"Total"=560`