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

Step-by-step solution

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 ! × 3 ! = 576