Question

The AccessPlus system at ISU has the following policy for creating a password:

-Passwords must be exactly 8 characters in length.

-Passwords must include at least one letter (a-z, A-Z) or supported special character (@, #, $ only).

-All letters are case-sensitive.

-Passwords must include at least one number (0-9).

-Passwords cannot contain spaces or unsupported special characters.

According to this policy, how many possible AccessPlus passwords are available? (Round to the nearest

trillion)

Answer 1

There are a total of 26*2 + 3 + 10 = 65 allowable characters here.

Total number of passwords with only digits is computed here as:
= 10*10*...... 8 times

= 10⁸

Total number of passwords with only 26*2 + 3 allowable characters and no digits is computed here as:
= 55*55*... 8 times
= 55⁸

Now total number of passwords without any conditions is computed here as:
= 65*65*.... 8 times as each of the 65 character can fill the 8 positions

= 65⁸

Therefore total number of passwords allowed here is computed as:
= 65⁸ - 10⁸ - 55⁸

= 234910775000000