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In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?

  1. $810$
  2. $1440$
  3. $2880$
  4. $50400$
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$\text{CORPORATION:}$ Total $11$ letters, and $R-2,O-3$

Vowel: $O – 3, A-1, I-1$

Now, $\underbrace{\underbrace{OOOAI}_{\frac{5!}{3!}}\;\;CRPRTN}_{\dfrac{7!}{2!}} \implies \dfrac{7!\cdot 5!}{3!\cdot 2!} = \dfrac{5040\cdot 120}{12} = 50400.$

So, the correct answer is $(D).$
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