One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming…
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?
105
525
945
1050
Solution
Non-zero digits: 9 choices. Vowels: 5. Consonants: 21. The password starts with a vowel and ends with a consonant, so the digit occupies the middle position. Number of passwords = $5 \times 9 \times 21 = 945$.