The number of six letter words (with or without meaning), formed using all the letters of the word &#39…

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 $=4!.\left(3!\right)$

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