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To solve this problem, let's break it down step by step.

### Step 1: Identify whether it is a **Permutation** or a **Combination** problem.

- A **combination** is when the order of items doesn't matter (e.g., selecting lottery numbers).
- A **permutation** is when the order of items does matter (e.g., arranging numbers in a specific order).

Since the digits are being arranged in a **lock** where the order matters (e.g., 123 is different from 321), this is a **permutation** problem, not a combination.

### Step 2: Determine the number of possible arrangements.

- The lock has **3 digits**, and each digit can be chosen from **0 to 9** (which gives 10 digits total: 0, 1, 2, ..., 9).
- However, the problem states that **no digit can be used twice**.

So, we calculate the number of arrangements as a permutation:
- For the first digit, there are 10 options (since any digit from 0 to 9 can be chosen).
- For the second digit, there are 9 options left (since one digit has already been used).
- For the third digit, there are 8 options left (since two digits have already been used).

Thus, the total number of permutations is:
\[
10 \times 9 \times 8 = 720
\]

### Step 3: Conclusion

The correct answer is **720 permutations**, since the order of digits matters and no digits are repeated.

#### Correct Answer: 
**C. 720; Permutation**

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Would you like more details or have any questions about this process?

Here are five related questions to expand your understanding:
1. How do you distinguish between a permutation and a combination in a problem?
2. What happens to the number of permutations if repetition of digits were allowed?
3. How would the solution change if the lock had 4 digits instead of 3?
4. What is the formula for calculating permutations in general?
5. How can you use factorial notation to simplify solving permutation problems?

**Tip**: In any permutation problem, remember that the order of selection matters!

A combination lock has a 3-digit combination made from the digits 0 - 9 without using the same digit twice. How many arrangements are possible? Decide whether this is a permutation or combination.

Solve the 3-digit combination lock problem using permutations. Learn how the total possible arrangements are calculated by applying the permutation formula when digits can't be repeated. Suitable for students in Grades 9-12.

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