The letters of the word EQUATION are arranged in such a way that <strong>ALL</strong> vowels as well as consonants are together. How many such arrangements are there?

Explanation

The word EQUATION has 5 vowels (E, U, A, I, O) and 3 consonants (Q, T, N). Grouping all vowels into one block and all consonants into another block gives 2 blocks. These blocks can be arranged in 2! ways. Inside the blocks, the vowels can be arranged in 5! = 120 ways and the consonants in 3! = 6 ways. Total ways = 2 \times 120 \times 6 = 1440.

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