# Q. 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

d. 1050

Correct Answer: c. 945

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

## To form a password, we need one non-zero digit, one vowel (in capital), and one consonant (in capital).

The password must start with a vowel and end with a consonant. Therefore, the password format will be Vowel-Digit-Consonant.

There are 5 vowels in the English alphabet (A, E, I, O, U).

There are 21 consonants in the English alphabet (the remaining letters after excluding the vowels).

There are 9 non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9).

For each position in the password, we can use the number of available options for that specific position. So, to calculate the total number of possible passwords, we can multiply the available options for each position:

Total passwords = Number of vowels × Number of non-zero digits × Number of consonants

Total passwords = 5 × 9 × 21

Total passwords = 945

Thus, 945 such passwords can be generated (option c).