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 :
Solution
<p>DAUGHTER</p>
<p>Total words $=8$ !</p>
<p>Total words in which vowels are together $=6!\times 3!$ words in which all vowels are not together</p>
<p>$$\begin{aligned}
& =8!-6!\times 3! \\
& =6![56-6] \\
& =720 \times 50 \\
& =36000
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
This question is part of PrepWiser's free JEE Main question bank. 135 more solved questions on Permutations and Combinations are available — start with the harder ones if your accuracy is >70%.