We want to see how many different 4-digit passwords we can create by using digits from 0 to 9, such that the first character can't be 0.
We will see that the correct option is D: 9,000
The total number of different combinations is given by the product between the number of options for each selection.
Here we have 4 selections.
- First character.
- Second character.
- Third character.
- Fourth character.
Now let's find the number of options for each of these:
- First character: 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- Second character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- Third character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- Fourth character: 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The total number of different combinations is just the product of these 4 numbers:
C = 9*10*10*10 = 9,000
So we can conclude that the correct option is D.
If you want to learn more about combinations, you can read:
https://brainly.com/question/2280026
