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This problem is about finding the probability of selecting 4 digits at random without replacement, in such a way that the digits match the first four digits of your phone number, assuming no repeats in your phone number.

### Step-by-step solution:

1. **Total digits to choose from:** The digits are taken from 0-9, so there are 10 possible digits.

2. **Order matters:** Since you're picking 4 digits and writing them in the order picked, the specific arrangement matters. This means we are dealing with permutations, not combinations.

3. **Probability calculation:**
   - The first digit of your phone number must match one of the 10 digits you can pick from. So, the chance of picking the correct first digit is \( \frac{1}{10} \).
   - After picking the first correct digit, there are only 9 digits left (since we pick without replacement). The chance of picking the correct second digit is \( \frac{1}{9} \).
   - For the third digit, there are 8 digits remaining, so the probability of picking the correct third digit is \( \frac{1}{8} \).
   - For the fourth digit, there are 7 digits left, so the chance of picking the correct fourth digit is \( \frac{1}{7} \).

4. **Multiply these probabilities together:**
   \[
   P = \frac{1}{10} \times \frac{1}{9} \times \frac{1}{8} \times \frac{1}{7} = \frac{1}{5040}
   \]

So, the probability of selecting the first four digits of your phone number in order is \( \frac{1}{5040} \).

Would you like further details or have any questions?

### Related Questions:
1. What would the probability be if you were picking 3 digits instead of 4?
2. How would the probability change if repetition of digits were allowed?
3. What is the probability of selecting any 4 digits in random order without replacement?
4. How does the number of possible arrangements of 4 digits change if the total digits available increase to 15?
5. How many different ways can you arrange the 4 digits if they are drawn from 10 digits?

**Tip:** When solving probability questions with permutations, always consider whether the order matters and whether replacement is involved!

You pick 4 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have written the first 4 digits of your phone number? Assume there are no repeats of digits in your phone number.

Find out the probability of randomly selecting 4 digits from 0-9 without replacement and matching the first four digits of your phone number. This problem covers core probability concepts and is ideal for students in Grades 9-12.

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