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?
- (a) 105
- (b) 525
- (c) 945 ✓ UPSC's answer
- (d) 1050
Why the answer is (c)
• The password consists of three distinct characters: one non-zero digit, one vowel, and one consonant.
• The first position is fixed for a vowel, and the last position is fixed for a consonant.
• There are 5 vowels (A, E, I, O, U) and 21 consonants in the English alphabet.
• The middle position must be occupied by a non-zero digit, which can be any of the 9 digits (1-9).
• The total number of passwords is the product of the choices for each position: 5 (vowels) × 9 (digits) × 21 (consonants) = 945.
Why the other options are wrong
- (a) 105
- 105 is incorrect because it likely results from using only 5 vowels and 21 consonants but incorrectly limiting the digit choices or miscalculating the product (e.g., 5 × 21 = 105, ignoring the digit).
- (b) 525
- 525 is incorrect because it corresponds to 5 × 5 × 21, which would imply only 5 choices for the middle character instead of 9 non-zero digits.
- (d) 1050
- 1050 is incorrect because it corresponds to 5 × 10 × 21, which incorrectly includes 0 as a valid non-zero digit choice for the middle position.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.