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

Answer:

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

Step-by-step 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.