Question

The selection of a password of a computer account has the followingrestrictions: The password must be 6, 7, or 8 characters long. A charactercan be lower case letter or a decimal digit. The first character must be alowercase letter. Determine the total number of possible passwords with thegiven restrictions

Answer 1

2,095,636,800,000 possible passwords.

Explanation:

There are:

26 lower case characters.

10 decimal digits.

Passwords with 6 characters:

The first character must be a lower case letter, so 26 possible outcomes.

Any of the other 6 - 1 = 5, there are 36 possible options. So

`T_(6) = 26*36^(5) = 1572120576`

Passwords with 7 characters:

Same logic as above, just the last 6 with 36 possible options. So

`T_(7) = 26*36^(6) = 56596340736`

Passwords with 8 characters:

7 with 36 possible options

`T_(8) = 26*36^(7) = 2037468300000`

Total:

`T = T_(6) + T_(7) + T_(8) = 1572120576 + 56596340736 + 2037468300000 = 2095636800000`

2,095,636,800,000 possible passwords.