A password of 4 letters is to be formed with vowels alone. How many such passwords are possible if.
(a) repetition of letters is allowed,
(b) repetition of letters is not allowed?

Explanation

The tasks `T_(1),T_(2),T_(3)` and `T_(4)` are about filling the 1st, 2nd,3rd and 4th slots in the password.
(a) The first slot can be filled in 5 ways (a,e,i,o or u).
The second can also be filled in 5 ways (with repetition being allowed).
The third and fourth can also be filled in 5 ways each.
Using the generalization, we get `5xx5xx5xx5=625` passwords.
(b) The first slot can be filled in 5 ways (a,e,i,o or u). The third and fourth in 3 and 2 ways respectively. thus the total number of possible passwords are `5xx4xx3xx2=120`.