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!