In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together?
Options:
A . 30
B . 48
C . 144
D . 576
E . None of these
Answer: Option D 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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