In how many ways can the letter of the word 'INSURANCE' be arranged, so that the vowels are never separate?

Explanation

The word 'INSURANCE' has nine different letters, combine the vowels into one bracket as (IUAE) and treating them as one letter we have six letters vix.
(IUAE)N S R N C and these can be arranged among themselves in `(6!)/(2!)` ways and four vowels within the bracket can be arranged themselves in 4! ways
`therefore`Required number of words`=(6!)/(2!)xx4!=8640`