Discrete Math Each user has a pin 4 characters long where ea

Discrete Math

Each user has a pin 4 characters long where each character is an uppercase letter, a lowercase letter, or a digit. Each password must contain at least one digit. How long will it take (these are, units of time) to check every possible character combination, if each check takes one unit of time?

Solution

Number of Uppercase letters = 26

Number of lowercase letters = 26

Number of Digits = 10

Number of 4 pin characters with all possible combinations = (26+26+10)^4 = 62^4

Number of 4 pin characters with no digits = (26+26)^4 = 52^4

Hence number of possible characters = 62^4 - 52^4 = 7464720 ways

Time taken will be 7464720 units of time