In how many ways can the letters of the word EQUATION be arranged if vowels and consonants occur together? 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.
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.