Multiple choice

The total number of words which can be formed using all the letters of the word "AKSHI" if each word begins with vowel or terminates with vowel

  1. $84$
  2. $12$
  3. $48$
  4. $60$
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A Correct answer
Explanation

Total permutations of AKSHI is 5! = 120. Words starting with a vowel (A, I): 2 * 4! = 48. Words ending with a vowel: 2 * 4! = 48. Words starting AND ending with a vowel: 2 * 1 * 3! = 12. By inclusion-exclusion, 48 + 48 - 12 = 84.

AI explanation

The word AKSHI has 5 distinct letters with 2 vowels (A, I) and 3 consonants. Using the principle of inclusion-exclusion, the number of words beginning with a vowel is 2 * 4! = 48, and the number of words ending with a vowel is also 2 * 4! = 48. The number of words beginning and ending with a vowel is 2 * 1 * 3! = 12. The total number of valid words is 48 + 48 - 12 = 84.

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