A 5-letter password is to be constructed from the following letters: A, B, C, D, and E and the password must contain exactly 3 of the letters. (Obviously at least one of them will need to be used more than once to create a 5-letter password.) you should show all your work and justify each computation.

(a) Suppose A,B, and C are the letters selected and we use A twice, B twice, and C once. How many different passwords exist in this scenario?

(b) Suppose A,B, and C are the letters selected and there are no other restrictions. How many different passwords exist in this scenario?

(c) Now suppose we don't put any restrictions on the letters chosen. (It could be A,B, and C, or it could be A, C, and D, or it could be B, D, and E, etc.) How many different passwords exist in this scenario?