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.