How many words with or without meaning can be formed using all the letters of the word "EQUATION" at a time if vowels and consonants occur together. My answer is $5!3!2!=1440$. Am I right?
In the word "EQUATION" there are 3 consonants (Q,T,N) so there are $3!$ ways to arrange and 5 vowels (E,U,A,I,O) so $5!$ ways to arrange. In whole for both first consonant and then vowels or vice-versa, there are $2!$ ways . so in total $2! \cdot 5! \cdot 3!=1440$ ways.