One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?

Here's a brief explanation: 1. **Identify the available choices for each character type:** * Non-zero digits: {1, 2, 3, 4, 5, 6, 7, 8, 9} = 9 options. * Vowels (capital): {A, E, I, O, U} = 5 options. * Consonants (capital): Total letters (26) - Vowels (5) = 21 options. 2. **Determine the password structure based on constraints:** The problem states that one non-zero digit, one vowel, and one consonant are to be used. This means each password will have exactly three characters. * Constraint 1: "each password has to start with a vowel." This fixes the first position. * Constraint 2: "and end with a consonant." This fixes the third position. * The remaining character type (the non-zero digit) must therefore occupy the middle position. So, the password structure is: Vowel - Non-zero Digit - Consonant. 3. **Calculate the total number of passwords:** * Number of choices for the first position (Vowel) = 5 * Number of choices for the second position (Non-zero Digit) = 9 * Number of choices for the third position (Consonant) = 21 Total passwords = (Choices for Vowel) * (Choices for Non-zero Digit) * (Choices for Consonant) Total passwords = 5 * 9 * 21 Total passwords = 45 * 21 Total passwords = 945 Therefore, 945 such passwords can be generated. The final answer is C) 945.