The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________.
Answer (integer)
576
Solution
Total possible words = 6! = 720
<br><br>When 4 consonants are together (V, W, L, S)
<br>such cases = 3! ⋅ 4! = 144
<br><br>All consonants should not be together<br><br>= Total $-$ All consonants together,<br><br>= 6! $-$ 3! 4! = 576
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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