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 generated?

Correct Option (C)

The problem requires forming a password with a specific structure: starting with a vowel, followed by a non-zero digit, and ending with a consonant. To determine the total number of such passwords, the fundamental principle of counting is applied by multiplying the number of choices available for each position.

• Number of choices for the first position (vowel): There are 5 vowels in the English alphabet (A, E, I, O, U).
• Number of choices for the second position (non-zero digit): There are 9 non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9).
• Number of choices for the third position (consonant): There are 21 consonants in the English alphabet (26 total letters - 5 vowels).

Therefore, the total number of possible passwords is calculated as:

Total Passwords = (Number of vowels) × (Number of non-zero digits) × (Number of consonants)

Total Passwords = 5 × 9 × 21 = 945.

Incorrect Options:

Options A (105), B (525), and D (1050) are incorrect. These values do not result from the accurate application of the fundamental principle of counting based on the specified constraints for password generation. The correct calculation, considering 5 vowels, 9 non-zero digits, and 21 consonants, yields 945 possible passwords, making these alternatives inconsistent with the problem's requirements.