Answer:
c) 20,000
Explanation:
Number of digits = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 = 10,
Number of vowel letters = a, e, i, o, u = 5
Repetition of digits is permitted but repetition of vowel letters is not permitted
Let the password be presented in dash form as shown below:
____ ____ ____ ____ ____ =
D D D V V
where:
D = possible number of digits to fill the spot
V = possible number of vowels to fill the spot
Since repetition of digits is permitted, each spot marked as D can be filled with any one of 10 digits from 0 - 9
The first spot marked V has 5 possible options (a, e, i, o, u) & the second spot marked V only has 4 possible options (since repetition of vowels is not permitted).
We then place the number of possibilities in each spot and multiply them to determine the number of passwords possible
10 * 10 * 10 * 5 * 4 = 20,000
Therefore, the number of possible passwords is 20,000