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JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Permutations and Combinations

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The number of words, which can be formed using all the letters of the word "daughter", so that all the vowels never come together, is
  1. (A)34000
  2. (B)37000
  3. (C)36000✓ Correct
  4. (D)35000

Answer: (C)

Solution

DAUGHTER has 8 distinct letters: vowels A, U, E and consonants D, G, H, T, R.

Total arrangements of all 8 letters: .

Arrangements with all three vowels together: treat AUE as one block, giving 6 units to arrange, with the vowels internally permuted:


Arrangements where the vowels never come together:

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Single correct option

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