Question

1. A company wants to impose a more secure password system for its employees to use on the company’s network. The current policy requires a minimum of seven characters. The system under consideration requires a minimum of eight characters. The new system will allow repetition of characters, but not doubling (e.g., the sequence 121 would be acceptable, but not 112).
   
   For both password systems, assume the following:
   • Only alphanumeric characters can be used in the passwords, without any spaces or symbols.
   • A lowercase letter is treated as a separate character from the uppercase equivalent.
   • Only letters on a standard American keyboard will be accepted.
   • Characters are used in a random order.

       Using these guidelines, calculate the following:

1. How many different passwords are possible for the current password requirements using seven characters?
2. How many different passwords are possible for the proposed password requirements using eight characters without any doubling?
3. Which option has more possible passwords? How many more? State your answer in terms of millions, billions, trillions, or quadrillions.
4. The same company may impose the requirement that each password include at least one lowercase letter, at least one uppercase letter, and at least one number, but would allow doubled and repeated characters. How many different passwords are possible using eight characters under this proposal?

Answer 1