Hey :)
The answer is 50400 ways
Because,
The word 'CORPORATION' has 11 letters.
It has the vowels 'O', 'O', 'A', 'I', 'O' in it and these 5 vowels should always come together.
These 5 vowels can be grouped and considered as a single letter. CRPRTN (OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Hope this helps!