Question

a three - character password is to be created by choosing characters from the digits 0 through 5 inclusive, vowels (a, e, o, u), or 5 special keyboard characters. if only one character category can be used at a time, rank the following from smallest to largest based on the number of possibilities for a password.

1. digit, digit, vowel
2. vowel, special character, vowel
3. special character, vowel, digit

a. 1, 3, 2
b. 2, 3, 1
c. 3, 2, 1
d. they are all equal

please select the best answer from the choices provided.
a b c d

Explanation:

Step1: Determine the number of choices for each category

• Digits: Digits are from 0 through 5, so there are \( 5 - 0 + 1 = 6 \) choices (0, 1, 2, 3, 4, 5).
• Vowels: Vowels are (a, e, o, u), so there are 4 choices.
• Special characters: There are 5 special characters.

Step2: Rank the number of possibilities

• Number of digit choices: 6
• Number of vowel choices: 4
• Number of special character choices: 5

Ranking from smallest to largest: Vowel (4) < Special Character (5) < Digit (6). So the order of the categories (vowel, special character, digit) corresponds to the number of possibilities 4, 5, 6. So the ranking of the categories (1: digit, 2: vowel, 3: special character) by their number of possibilities (smallest to largest) is vowel (2), special character (3), digit (1), which matches option b (2, 3, 1).

Answer:

b. 2, 3, 1