Question

The number of six letter words (with or without meaning), formed using all the letters of the word ${}^{\prime }VOWEL{S}^{\prime },$ so that all the consonants never come together, is

Answer 1

Total possible words $=6!=720$
When $4$ consonants are together $(V,W,L,S)$
Total case when consonants are together
$O,E,\begin{array}{c}VWLS\end{array}$
Such cases $=3!\cdot 4!=144$
Required cases $=720-144=576$