A website requires users to set up an account that is password protected. If the password format is four letters followed by a single digit number, how many different passwords are possible?
Question
A website requires users to set up an account that is password protected. If the password format is four letters followed by a single digit number, how many different passwords are possible?
Solution
To solve this problem, we need to understand that each character in the password can be chosen independently.
Step 1: Determine the number of possibilities for each character.
- For the letters, since there are 26 letters in the English alphabet and they can be either lower case or upper case, we have 26*2 = 52 possibilities for each letter.
- For the digit, since there are 10 digits (0-9), we have 10 possibilities.
Step 2: Determine the total number of possibilities.
- Since the password format is four letters followed by a single digit number, the total number of possibilities is (number of possibilities for a letter)^4 * (number of possibilities for a digit).
- So, the total number of possibilities is 52^4 * 10 = 7311616000.
Therefore, there are 7311616000 different passwords possible.
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