Cosmological Conundrum

Why are all of the planets in our solar system in the same plane?  Space is three dimensional... what are the odds that all of the planets ended up in the same two dimensional plane?

Imagine a giant ball of dust floating in space.  Gravity pulls it together into a large spinning mass.   As the dust spins, it stretches out due to centrifugal force, like water flying off of a spinning top. You can think of Saturn as a microcosm of our early galaxy.  This is where the two dimensional plane comes into the picture. Now that the dust is in this flat spinning pancake, small amounts begin to clump up again due to gravity and eventually form our planets.