Final answer:
To determine how many 4-digit codes can be made with the digits 0-9, we calculate 10 options for each of the four positions, resulting in 10,000 unique combinations.
Step-by-step explanation:
To calculate how many 4-digit codes you can make using the numbers 0-9, we need to consider that the codes are comprised of four positions which can each take any digit from 0 to 9. However, since codes can start with the digit 0, we need to use a different approach from calculating permutations where order matter and no repetitions are allowed, such as with the factorial method (e.g., 4!). In this case, each of the four positions in the code can be filled by any of the 10 digits independently.
Calculating the total number of combinations:
- For the first position, there are 10 choices (0-9)
- For the second position, there are another 10 choices
- This pattern continues for the third and fourth positions
So, the total number of 4-digit codes is: 10 x 10 x 10 x 10 = 10,000.