Question

Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible?
34
40
5,040
10,000

Answer 1

To determine how many different four-digit passwords Geraldine can create using the digits 0 through 9, with each digit being used only once, we can break down the process:

1. **Choose the first digit:** There are 10 possible digits (0 through 9).
2. **Choose the second digit:** After selecting the first digit, there are 9 remaining digits available.
3. **Choose the third digit:** After selecting two digits, there are 8 remaining digits.
4. **Choose the fourth digit:** After selecting three digits, there are 7 remaining digits.

To find the total number of different passwords, we multiply the number of choices available at each step:

\[
10 \text{ (choices for the first digit)} \times 9 \text{ (choices for the second digit)} \times 8 \text{ (choices for the third digit)} \times 7 \text{ (choices for the fourth digit)}
\]

Calculating this gives:

\[
10 \times 9 \times 8 \times 7 = 5040
\]

Thus, the total number of different four-digit passwords possible is **5,040**.

The answer is therefore:

**5,040**