Ruth has the following set of refrigerator magnets: {A, B, C, D, E, F, G}.

How many different three-letter strings can she form with these magnets?

To solve this, we need to determine how many different three-letter strings can be formed from the given set of refrigerator magnets \(\{A, B, C, D, E, F, G\}\). 

### Assumptions:
- **Order matters** because we are forming strings. For example, "ABC" is different from "CBA".
- **Repetition is not allowed** because each magnet can only be used once in a string.

This problem requires calculating the **number of permutations** of 3 letters chosen from a set of 7.

### Formula for permutations:
The formula to calculate permutations is:

\[
P(n, r) = \frac{n!}{(n-r)!}
\]

Where:
- \(n\) is the total number of items (7 magnets),
- \(r\) is the number of items to select (3 letters).

### Substituting values:
\[
P(7, 3) = \frac{7!}{(7-3)!} = \frac{7!}{4!}
\]

Simplifying further:
\[
7! = 7 \times 6 \times 5 \times 4!
\]
\[
P(7, 3) = \frac{7 \times 6 \times 5 \times 4!}{4!} = 7 \times 6 \times 5 = 210
\]

### Final Answer:
Ruth can form **210 different three-letter strings** with her magnets.

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Would you like a detailed breakdown or visual representation of this? Here are related questions you might explore:

1. How many two-letter strings can Ruth form using the same set of magnets?
2. What if repetition is allowed—how many three-letter strings can be formed?
3. How many three-letter strings can be formed if order does not matter (combinations)?
4. If Ruth only uses vowels in her set (assuming they are given), how many three-letter strings could she form?
5. How many four-letter strings can Ruth form with the given set of magnets?

**Tip:** For permutation problems, always clarify if repetition is allowed and whether order matters before solving!

Ruth has the following set of refrigerator magnets: {A, B, C, D, E, F, G}. How many different three-letter strings can she form with these magnets?

Discover how to calculate the number of three-letter strings that can be formed using the set {A, B, C, D, E, F, G}. Learn about permutations, factorials, and the counting principle with step-by-step guidance. Suitable for Grades 8-10.

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