Peter's neighbour, Paul likes tulips. He would like to plant 2 white, 5 red and 6 black tulips in a row in a way such that a red and a black tulip cannot be next to each other. How many different ways can he design the row?

I count two cases:

1. …w…w…

bwrwb in which wrw takes 7 positions and it can start from 7 different places.

rwbwr wbw takes 8 positions and can start from 6 different places.

2. …ww…

red ww black

black ww red Which is 2 ways

So in Total I got $7+6+2=15$ ways. But the answer is 33 ways. I can’t think of any other ways of arrangement…