What is the number of positions of a 15 puzzle (4x4 board)

I wonder if someone can help me get a number for possible positions for this childs game of 15 sliding pieces in a 4x4 board.

The normal game has numbers 1-15 that need to be sorted. The board I want to calculate has only three kind of pieces: 6 red, 6 green, 3 black, and of course the empty slot you can move through.

I referred to this post and came up with this solution $\binom{16}{6}\binom{10}{6}\binom{4}{3}=6.726.720$. Does that look correct, or did I miss something?

from Hot Weekly Questions - Mathematics Stack Exchange