The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .
Answer (integer)
120
Solution
Consonants $\to$ LTTR
<br>Vowels $\to$ EE
<br><br>Total No of words = ${{6!} \over {2!2!}}$ = 180
<br><br>Total no of words if vowels are together
<br>= ${{5!} \over {2!}}$ = 60
<br><br>$\therefore$ Total no of words where<br> vowels never come together = 180 – 60 = 120.
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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