Solved on Jan 18, 2024
Find the number of unique passwords with 2 digits, where each digit can be a number or a letter.
Solution: There are 10 digits (0-9) and 26 letters (A-Z), so each digit can be chosen from 36 possibilities. Therefore, the total number of possible passwords is .
STEP 1
Assumptions
1. Each digit in the password can be a number (0-9) or a letter (A-Z, a-z).
2. There are 10 possible numbers (0-9).
3. There are 26 possible uppercase letters (A-Z) and 26 possible lowercase letters (a-z).
4. The password is exactly two characters long.
5. Each position in the password can be filled independently of the other.
STEP 2
First, we need to find the total number of possibilities for each digit in the password. Since each digit can be a number or a letter, we add the number of possibilities for each category.
STEP 3
Now, plug in the given values for numbers, uppercase letters, and lowercase letters to calculate the total possibilities for each digit.
STEP 4
Calculate the total possibilities for each digit.
STEP 5
Since the password is two digits long, and each digit can be chosen independently, we need to calculate the total number of different passwords by multiplying the total possibilities for the first digit by the total possibilities for the second digit.
STEP 6
Plug in the values for the total possibilities for each digit to calculate the total number of different passwords.
STEP 7
Calculate the total number of different passwords.
There are 3,844 different passwords that can be made.
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