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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?

Correct Answer: 50400

Explanation:

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 = 7! = 2520.
2!


Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged



in 5! = 20 ways.
3!


∴ Required number of ways = (2520 x 20) = 50400.



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