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

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Given word 'VOWELS'

Number of words Arranging all the letters $= 6!$

In the given word Consonants are W, L, S.

Treating all the consonants as one unit then number of units will be $4 .$

No of such arrangements $= 4! . (3!)$

VOWELS all the consonants never come together $=$ Total - all consonants come together $= 6! - 4! \times 3! = 576$

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