An audio equipment store has eleven different amplifiers, five tuners, six turntables, nine tape decks, six compact disc players, and thirteen speakers. Assuming that all components are compatible with each other, how many different complete stereo systems are available?

To determine the total number of different complete stereo systems available, you simply need to multiply the number of available options for each component. A complete stereo system includes one of each component: an amplifier, a tuner, a turntable, a tape deck, a compact disc player, and a speaker.

Given:
- 11 different amplifiers
- 5 different tuners
- 6 different turntables
- 9 different tape decks
- 6 different compact disc players
- 13 different speakers

The total number of different complete stereo systems can be calculated as:

\[
\text{Total systems} = (11 \times 5 \times 6 \times 9 \times 6 \times 13)
\]

Let's calculate this.The total number of different complete stereo systems available is \( 231,660 \).

Would you like to explore any details or have further questions?

Here are some related questions:

1. What if some components are incompatible with others?
2. How does the number of systems change if one component is removed?
3. How would the total change if the store added more options for one component?
4. What if the store had fewer options for each component?
5. Can this problem be solved using combinatorial methods?
6. How does this problem relate to permutations and combinations?
7. What if each stereo system had to include two of the same component, like two speakers?
8. What if there were restrictions on which components could be used together?

**Tip:** When dealing with independent choices across categories, multiply the number of options in each category to find the total number of combinations.

Learn how to calculate the total number of different complete stereo systems available by multiplying the options for amplifiers, tuners, turntables, tape decks, compact disc players, and speakers. Explore a detailed solution for this combinatorial problem.

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