The owner of a stereo store wants to advertise that

Wayne Steele

Wayne Steele

Answered question

2022-05-26

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 & Explanation

Arianna Turner

Arianna Turner

Beginner2022-05-27Added 12 answers

Step 1
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
Step 2
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 × N CD Player
7 × 8 = 56
different combinations! Now, we'll add ANOTHER layer of complexity by considering the options for speakers:
C Total = N Speaker × N Receiver × N CD Player
C Total = 10 × 7 × 8
C Total = 560

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