QJEEM25Ma2190: JEE Main 2025 Mathematics - Class 11 JEEM25Ma2190 Solution: The number of words, which can be formed using all the letters…

Question

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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 :

Accepted Answer

DAUGHTER

Total words $=8$ !

Total words in which vowels are together $=6!\times 3!$ words in which all vowels are not together

$\begin{aligned} = 8! - 6! \times 3! \\ = 6! [56 - 6] \\ = 720 \times 50 \\ = 36000 \end{aligned}$

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