Why do objects all orbit in the same direction? In a solar system or a planet that has many moons, why do their orbiting objects all orbit in the same direction?

Is it possible for two orbiting masses to orbit in the opposite direction of each other?
This video provides a visual answer: https://youtu.be/MTY1Kje0yLg?t=3m24s
objects orbiting in different directions are more likely to collide with each other. By the process of elimination, eventually one direction of orbit dominates.