$(15\%)$ A system allows a user to choose a password with a length of one to eight characters, inclusive. Assume the selection of any password is equiprobable. If an attacker performs a dictionary attack using a computer that can test $10,000$ passwords per second, determine

the average time in hours for the attacker to find a password for each of the following conditions.

a$.$ Password characters must be numbers $("0"$ to $"9").$

b$.$ Password characters may be any alphanumeric characters $("A"$ through $"Z,""a"$

through $"z,"$ and $"0"$ through $"9").$

c$.$ Password characters may be any ASCII characters from $1$ to $127,$ inclusive.