JEE MAIN - Mathematics (2021 - 31st August Morning Shift - No. 21)
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
576
Explanation
Total possible words = 6! = 720
When 4 consonants are together (V, W, L, S)
such cases = 3! ⋅ 4! = 144
All consonants should not be together
= Total $$-$$ All consonants together,
= 6! $$-$$ 3! 4! = 576
When 4 consonants are together (V, W, L, S)
such cases = 3! ⋅ 4! = 144
All consonants should not be together
= Total $$-$$ All consonants together,
= 6! $$-$$ 3! 4! = 576
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