We want to find the maximum number of different passwords that Brad can have. We know that the password must be five digits long, and it can use the numbers 0-9. With this information we can see that we have 10 choices for each digit.
\begin{gathered}
\boxed{1^\text{st} \text{ Digit}} \ \ \ \boxed{2^\text{nd} \text{ Digit}} \ \ \ \boxed{3^\text{rd} \text{ Digit}} \ \ \ \boxed{4^\text{th} \text{ Digit}} \ \ \ \boxed{5^\text{th} \text{ Digit}} \\
10 \qquad \qquad 10 \qquad \quad 10 \qquad \qquad 10 \qquad \quad 10 \\
\text{ choices} \quad \ \ \text{ choices} \quad \ \ \text{ choices} \quad \ \ \text{ choices} \quad \ \ \text{ choices} \\
\end{gathered}
However, we are also told that the digits should not repeat. Therefore, after determining a number for the first digit we cannot use this number for the other digits. This means that after each digit we will reduce the number of choices by one.
Number of Choices for the First Digit
10
Number of Choices for the Second Digit
9
Number of Choices for the Third Digit
8
Number of Choices for the Fourth Digit
7
Number of Choices for the Fifth Digit
6
Because we have the number of possible outcomes of each event, we will use the Fundamental Counting Principle to find the maximum number of different passwords.
10 * 9 * 8 * 7 * 6 = 30 240
The maximum number of choices for the password is 30 240, so the correct option is G.
