A computer password consists of eight characters.

a. How many different passwords are possible if each character may be any lowercase letter or digit?

b. How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit?

c. A computer system requires that passwords contain at least one digit. If eight characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the probability that a valid password will be generated?

Answer :

Step 1 of 3 :

Given,

The computer consists of 8 character password.

The claim is to find how many passwords are possible if each character may be any lowercase letter or digitA computer keyboard contains 26 letters and 10 digits

Totally 36 characters

The size of the password be 8 characters

Therefore = 2.8211

There are 2.8211 passwords are possible if each character may be any lowercase letter or digit.

Step 2 of 3 :

b)

The claim is to find how many passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit.

There are 2.8211 passwords are possible if each character may be any lowercase letter or digit.

There are 26 alphabets, that is

- = 2.6122

Therefore, 2.6122 passwords are possible.