How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Explanation

There are 5 vowels and 3 consonants in the word 'EQUATION'. If all 5 vowels occur together and all 3 consonants occur together then taking them as one-one letter, no. of ways to arrange them
`= .^(2)P_(2) =2! = 2`
Again, no of ways of arranging 5 vowels `= 5! = 120`
No. of ways of arranging 3 consonants `= 3! = 6`
Therefore, total no. of words `= 2 xx 120 xx 6 = 1440`.