JEE MAIN - Mathematics (2025 - 23rd January Morning Shift - No. 3)
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 :
34000
37000
35000
36000
Explanation
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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