Let's analyze the problem and solve it step by step.

Question Analysis:

• Problem Setup: Sara needs to set a 4-digit passcode using the numbers 0–9.
• Key Consideration: The order of the digits in the passcode matters. For instance, "1234" is different from "4321." This implies that this is a permutation problem, not a combination.

Key Formula:

The number of possible passcodes can be calculated by finding the permutations of 4 digits chosen from a total of 10 digits. When repetitions are allowed (as nothing in the question says otherwise), the formula for permutations is:

$n^r$

Where:

• $n$ = total number of available choices (10 digits: 0–9),
• $r$ = number of digits chosen (4 digits).

Calculation:

$10^4 = 10 \times 10 \times 10 \times 10 = 10,000$

Final Answer:

• Classification: Permutation
• Number of Passcodes: 10,000

Would you like further clarification? Let me know if you need additional examples or a breakdown!

Related Questions:

1. What is the difference between permutations and combinations, and when do we use each?
2. How would the answer change if repetitions were not allowed?
3. What would the total number of codes be if the passcode length were increased to 6 digits?
4. If Sara wanted to use only even digits, how many passcodes would be possible?
5. How do we compute permutations when using only a subset of digits (e.g., 5 digits instead of 10)?

Tip:

Remember, permutations are used when order matters (e.g., passcodes, rankings), while combinations are for cases where order does not matter (e.g., selecting a group of items).