Step-by-step Solution:

The word "CORPORATION" has 11 letters with vowels O, O, A, I, O and consonants C, R, P, R, T, N.
1. Treat the vowels as a single unit, reducing the problem to 7 units (vowel group + 6 consonants).
2. Arrange these 7 units: \( \frac{7!}{2!} = 2520 \) (since R repeats).
3. Arrange the 5 vowels within their unit: \( \frac{5!}{3!} = 20 \) (since O repeats).
4. Multiply: \( 2520 \times 20 = 50,400 \).
Thus, the total arrangements keeping vowels together = 50,400.