Question

Each user has a password 6 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 to check every possible character combination, if each check takes one unit of time?

Answer 1

Answer:

$36^{6} -26^6$

Step-by-step explanation:

We have 36 characters in total which we can use in order to form a 6 character password.

For each place in this password we have choice of 36 of them, so, the total number of possible passwords of 6 characters is:

$36*36*36*36*36*36=36^6$

But, we have to exclude all passwords which have no numbers because, by the task, the password must contain at least one digit.

So, now we have choice of 26 characteristic to form password without digits and get $26^6$ passwords like that, contained just of letters without digits.

So, the final answer is that we have $36^6-26^6$  6-character passwords with at least one digit.