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NDA 2025 · PYQ · Permutations and Combinations · easy

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

  1. A.6
  2. B.9
  3. C.12✓ Correct
  4. D.24

Explanation

DELHI has 5 letters: D, E, L, H, I. Vowels: E, I (positions 2 and 5). Consonants: D, L, H (positions 1, 3, 4). Keeping positions of vowels and consonants unchanged means vowels are arranged in vowel positions and consonants in consonant positions. Vowels: 2! = 2 ways. Consonants: 3! = 6 ways. Total = 2·6 = 12.
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