Calculating valid password combinations with structural and character constraints
Question
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?
Options
105
525
945
1050
Explanation
Establish the structural template for the 3-character password based on the strict positional constraints: `[Vowel] [Digit] [Consonant]`.
Calculate the available pool for each independent slot:
Multiply the independent probabilities: Total permutations = 5 × 9 × 21 = 45 × 21 = 945.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q76
Section
Numerical Ability
Sub-topic
Permutations & Combinations
Type
Factual single
Difficulty
Medium
Source hint
Password with vowel, consonant, non-zero digit
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