Zero. You can't fill such board with 31 dominos.

Even if we could, we still couldn't find how many ways there are because a set of dominos up to 9 makes 36 dominos and we take 31 of them. But the possibilities depend on the dominos we choose.

The proof of this is easy. Assume we have the chessboard below:

Now, how many tiles left? 30 white and 32 black.

But every domino will cover 1 white and 1 black tile. They can cover 31 white and 31 black, but not 30 white and 32 black. Thus it's impossible to fill such board.