QUESTION

CSAT

Hard

Maths

Prelims 2022

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?

Select an option to attempt

Explanation

We are tasked with forming passwords using three components:

  1. One non-zero digit
  2. One vowel
  3. One consonant

The password must start with a vowel and end with a consonant. Here's how we can break it down:

Non-zero digits: There are 9 possible non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9). Vowels: There are 5 vowels in the English alphabet (A, E, I, O, U). Consonants: There are 21 consonants in the English alphabet.

The structure of the password is: The first character must be a vowel (55 options). The second character must be a non-zero digit (99 options). The third character must be a consonant (2121 options).

Thus, the total number of passwords that can be generated is: Total number of passwords = 5×9×21=9455 \times 9 \times 21 = 945

Therefore, the correct answer is 945945.

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