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
Solutions · 1
Official solution
VOWELS has 2 vowels (O, E) and 4 consonants (V, W, L, S), all distinct.
Total arrangements: 6!=720.
All consonants together: treat as one block, arrange with 2 vowels: 3! units ×4! internal =6×24=144.
\[\text{Required} = 720-144 = 576\]