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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!/2!= 2520.


 


Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 3!/5!= 20 ways.


 


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


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