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In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together?

In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together? Correct Answer 576

The given word contains 7 different letters.
Keeping the vowels (AUIO) together, we take them as 1 letter.
Then, we have to arrange the letters CTN (AUIO).
Now, 4 letters can be arranged in 4! = 24 ways.
The vowels (AUIO) can be arranged among themselves in 4! = 24 ways.
∴ Required number of ways = (24 × 24) = 576

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