Question

29. repetition of digits is permitted and the letters must be 2 DIFFERENT vowels (a, e, i, o, u).

Answer 1

Answer:

c) 20,000

Step-by-step 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