Permutation and Combination: The number of words, which can be formed using all the letters of… | JEE Main 2025 | Yukti Vault

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JEE Main 2025 (Online) 23rd January Morning ShiftQuestion 1

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 :

Permutation and Combination

$34000$$37000$$35000$$36000$✓ Correct answer

Solution

All $8$ letters are distinct: $8!=40320$; with the vowels A, U, E together: $6!\cdot3!=4320$. So $40320-4320=36000$.

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