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

In how many different ways can the letters of the word 'CORPORATION' be arranged sothat the vowels always come together Correct Answer 50400

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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