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

LohaHridoy
  1. 810
  2. 1440
  3. 2880
  4. 50400
  5. 5760

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AhmedNazir

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Answer: Option 4

In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN (OOAIO). This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different. Number of ways arranging these letters = $$\frac{{7!}}{{2!}}$$ = 2520 Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in $$\frac{{5!}}{{3!}}$$ = 20 ways ∴ Required number of ways = (2520 x 20) = 50400

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