You pick 3 digits \( (0-9) \) at random without replacement, and write them in the order picked. What is the probability that you have written the first 3 digits of your phone number? Assume there are no repeats of digits in your phone number. Give your answer as a reduced fraction.

To determine the probability that the three digits you randomly pick match the first three digits of your phone number, let's break down the problem: 1. **Total Possible Outcomes:** - There are 10 possible digits (0-9) for the first digit. - Since you're picking without replacement, there are 9 remaining digits for the second digit. - Similarly, there are 8 remaining digits for the third digit. - Therefore, the total number of possible ordered sequences of three distinct digits is: \[ 10 \times 9 \times 8 = 720 \] 2. **Favorable Outcome:** - There is only **one** specific sequence of three digits that matches the first three digits of your phone number. 3. **Probability Calculation:** - The probability \( P \) is the ratio of the favorable outcome to the total possible outcomes: \[ P = \frac{1}{720} \] - This fraction is already in its simplest form. **Final Answer:** \(\boxed{\dfrac{1}{720}}\)