How many arrangements are there of the word “PERMUTATIONS” so that no three vowels come together?

Question

I did this-

Total Arrangements without any constraint - Total arrangements when 3 Vowels together = Total arrangements when no 3 vowels are together.

$\frac{12!}{2} - (\frac{10!}{2} \cdot {}_5C_3 \cdot 3\cdot2) = 130636800$.

But the answer seems wrong. What am I doing wrong? I need help.