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Q76·CSAT · Prelims 2022

Calculating valid password combinations with structural and character constraints

NumericalPermutations & CombinationsFactual singleMedium

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

a

105

b

525

c

945

Answer
d

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:

Slot 1 (Vowel): There are exactly 5 vowels in the English alphabet (A, E, I, O, U).
Slot 2 (Non-zero digit): There are exactly 9 non-zero digits (1 through 9).
Slot 3 (Consonant): There are exactly 21 consonants in the 26-letter English alphabet.

Multiply the independent probabilities: Total permutations = 5 × 9 × 21 = 45 × 21 = 945.

For rigidly ordered security codes, directly multiply the raw element counts of each isolated slot category together.

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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