Predictability in Number Systems-^V?

The other main area where Pascal's Triangle shows up is in Probability, where it can be used to find Combinations. Let's say you have five hats on a rack, and you want to know how many different ways you can pick two of them and wear them. It doesn't matter to you which hat is on top, it just matters which two hats you pick. So this problem amounts to the question "how many different ways can you pick two objects from a set of five objects?"

The "marble drop" would speak to this as a probabilistic determination, and mathematical described in recognizing Pascal's triangle? Which path?

http://www.rand.org/methodology/stat/applets/clt.html

Using marble drops to help visualize these pathways, the proof of Stefan Boltzman in the binomal series, speaks to the chaos generated from considering such probabilties?

http://www.physicsforums.com/archive/t-22217

Long time no see