14) Carla has forgotten the login password for her brand new computer! However, she remembers that it is a sequence of 4 vowels, not necessarily distinct, of which two are uppercase and two are lowercase. How many different passwords, at most, does Carla need to try to turn on the computer?
(A) $3 \cdot 5^{4}$,
(B) $5^{5}$,
(C) $6 \cdot 5^{4}$,
(D) $5^{6}$,
(E) $3 \cdot 5^{6}$.
14. The answer is $(\mathbf{C})$.

The possible arrangements of uppercase and lowercase letters in the password are 6:

$$
M M m m, m m M M, M m M m, m M m M, m M M m, M m m M \text {, }
$$

where $M$ indicates an uppercase letter and $m$ indicates a lowercase letter. For each of these arrangements, each of the 4 letters can take 5 distinct values, so each arrangement results in $5^{4}$ possibilities. Consequently, there are $6 \cdot 5^{4}$ possible passwords that meet the required characteristics. This is the maximum number of passwords Carla needs to try before she can turn on the computer.

[Problem proposed by D. Lombardo.]