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

Answer: Option D

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