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

In how many different ways can the letters of the word SOFTWARE be arranged in such a way that the vowels always come together? Correct Answer 4320

The given word contains 8 different letters.
We keep the vowels (OAE) together and treat them as 1 letter.
Thus, we have to arrange the 6 letters SFTWR(OAE)
These can be arranged in 6! = 720 ways
The vowels (OAE) can be arranged among themselves in 3! = 6 ways.
∴ Required number of ways = (720 × 6) = 4320

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