A witness described a getaway car as having a NSW registration plate starting with TLK. The witness
could not remember the three digits that followed, but recalled that all three digits were different.
Calculate how many cars in NSW could have a registration plate with these letters and numbers.

To solve this problem, we need to determine how many unique combinations of three different digits can follow the prefix "TLK" on a New South Wales (NSW) registration plate.

### Step-by-Step Calculation

1. **Understanding the Registration Format**: 
   - The registration plate starts with "TLK".
   - This is followed by three digits (denoted as \(D_1D_2D_3\)).

2. **Requirement for the Digits**:
   - All three digits \(D_1, D_2, D_3\) must be different.
   - Each digit can be any value from 0 to 9.

3. **Calculating the Number of Combinations**:
   - For the first digit \(D_1\), there are 10 possible choices (0 through 9).
   - For the second digit \(D_2\), there are 9 remaining choices since it must be different from \(D_1\).
   - For the third digit \(D_3\), there are 8 remaining choices since it must be different from both \(D_1\) and \(D_2\).

4. **Total Number of Combinations**:
   \[
   \text{Total combinations} = 10 \times 9 \times 8
   \]

Now, let's calculate this:

\[
10 \times 9 \times 8 = 720
\]

### Conclusion

There are **720 different possible NSW registration plates** that start with "TLK" and have three different digits following it.

Would you like any more details or have any questions?

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Here are some related questions you might find interesting:

1. What if the registration plate had four different digits instead of three?
2. How many combinations would there be if the digits could repeat?
3. What is the probability of randomly guessing the correct registration plate under these conditions?
4. How does this calculation change if the registration plate includes letters after the digits?
5. How many unique registration plates are possible with a prefix of any three letters followed by any three digits?

**Tip:** When calculating combinations where repetition is not allowed, always reduce the number of choices as you select each item.

Discover how many cars in New South Wales (NSW) could have a registration plate starting with TLK followed by three unique digits. Learn the step-by-step calculation method and understand the total number of combinations possible under these conditions.

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