Question

You need to create a password for your new email account. It must consist of 3 letters followed by 4 digits. You can repeat letters and numbers. How many different passwords can you create?

Answer 1

175,760,000

Step-by-step explanation:

You can multiply together the number of possibilities for each part of the password. Since there are 26 letters and 10 digits to choose from, the calculation is 26 • 26 • 26 • 10 • 10 • 10 • 10.

Answer 2

Each password:

[letter] [letter] [letter] [digit] [digit] [digit] [digit]

The first letter can be any one of 26 .
For each of those . . .
The second letter can be any one of 26 .
For each of those . . .
The third letter can be any one of 26 .
For each of those . . .
The first digit can be any one of 10.
For each of those . . .
The second digit can be any one of 10.
For each of those . . .
The third digit can be any one of 10.
For each of those . . .
The fourth digit can be any one of 10.

Total number of possible assortments =

(26) · (26) · (26) · (10) · (10) · (10) · (10)

= 175,760,000