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In how many ways can the letter of the w...

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

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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`
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