A person need to make up a four-digit code to open the lock on the garage door. If the person decides to use four digits from the first four digits (0 through 3), how many different codes can be made?


To determine how many different four-digit codes can be made using the digits 0 through 3, we can approach this problem step by step.

### Key points:
1. **Four digits to choose from**: The available digits are 0, 1, 2, and 3.
2. **Four-digit code**: The code must consist of four digits.
3. **Repetition allowed**: The problem does not mention any restriction against repeating digits, so each of the four digits can be used in any position of the code.

### Calculation:
For each of the four positions in the code, you have 4 choices (0, 1, 2, or 3).

- For the first position: 4 choices (0, 1, 2, or 3)
- For the second position: 4 choices (0, 1, 2, or 3)
- For the third position: 4 choices (0, 1, 2, or 3)
- For the fourth position: 4 choices (0, 1, 2, or 3)

Since each position in the code is independent, the total number of different codes is:

\[
4 \times 4 \times 4 \times 4 = 4^4 = 256
\]

Thus, the person can create **256 different codes**.

Would you like more details or further explanation?

### Related questions:
1. What if repetition of digits is not allowed? How many codes could be made?
2. How many codes could be made if we used digits from 0 to 5 instead?
3. What is the probability of guessing the correct code on the first attempt?
4. How many 3-digit codes can be made using digits 0 through 3?
5. If each code digit could only be odd (1 or 3), how many codes are possible?

### Tip:
For problems involving combinations of digits or letters, always check if repetition is allowed, as this significantly impacts the total count.

A person needs to make up a four-digit code to open the lock on the garage door. If the person decides to use four digits from the first four digits (0 through 3), how many different codes can be made?

Discover how to calculate the total number of different four-digit codes that can be made using digits 0, 1, 2, and 3. This combinatorics problem teaches the concept of permutations with repetition, suitable for students in Grades 6-8.

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