Question

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

a) 6,760,000

b) 3,276,000

c) 20,000

d) 6760

Answer 1

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