# 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?

• Looks OK to me. There are only 2 groups, 5 distinct vowels and 3 distinct consonants which can be independently permuted and the groups themselves can be permuted. – Shailesh Sep 12 '15 at 14:51

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.
• Welcome to Math.SE. This Question is almost two years old, and essentially you repeat the confirmation requested by the Question given in a previous Comment, but you are certainly allowed to do so. However I'd encourage you to improve the formatting, both as to capitalization and punctuation/spacing, and learn to post with mathematical expressions using $\LaTeX$. – hardmath Jun 15 '17 at 4:57