A system allows the user to choose a password with a length of one to eight characters, inclusive. Assume that 10,000 passwords can be tested per second. The system administrators want to expire passwords once they have a probability of 0.10 of having been guessed. Determine the expected time to meet this probability under each of the following conditions.
a. Password characters may be any ASCII characters from 1 to 127, inclusive.
b. Password characters may be any alphanumeric characters ("A" through "Z," "a" through "z," and "0" through "9").
c. Password characters must be digits.