put 4 red, blue and green triangles in a row How many ways are there to put 4 red, 4 blue and 4 green triangles in a row so that no blue triangles would lie next to each other.

I got an answer, there are 126*56=7056 combinations. Could you check please, if the answer is right/wrong?
HINT: Do the problem in two steps.


First determine in how many ways the red and green triangles can be arranged in a row. 
Each of those ways is a row of eight triangles; counting the spaces at the beginning and end of the row, there are nine slots into which you can insert a blue triangle. Since you’re not allowed to have two blue triangles in a row, you can put at most one blue triangle into a slot. How many ways are there to choose four of the nine slots to be filled with blue triangles?


Now what must you do with the answers to (1) and (2) to answer your problem?
total there are $\frac{12!}{(4!)^3}$ combination no.of combination and  the blue triangle will lie next to each other =$\frac{11!}{3!4!4!}$ in conclusion there will be 23100