Mathematics · Permutations and Combinations

JEE Main 2025 — 23 January, Morning Shift — Question 12

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

Answer: C

DAUGHTER

Total words $=8$ !

Total words in which vowels are together $=6!\times 3!$

words in which all vowels are not together

$=8!-6!\times 3!$

$=6![56-6]$

$=720 \times 50$

$=36000$

Answer key and solution verified before publishing.

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