Q38 / 75 · JEE Main 2025 (23 Jan Shift 1) · Mathematics

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

Correct answer
A
$36000$
B
$37000$
C
$34000$
D
$35000$

Solution

DAUGHTER Total words $=8$ ! Total words in which vowels are together $=6!\times 3!$ words in which all vowels are not together $\begin{aligned} & =8!-6!\times 3! \\ & =6![56-6] \\ & =720 \times 50 \\ & =36000 \end{aligned}$ Ans.(3)

Hence, the correct answer is option: 'A'.

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