Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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BinomialDistribution

The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.

To get a result of X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q (1-p), then X heads and N-X tails has a probability calculated by multiplying X p's times N-X q's or (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/X!/(N-X)! different combinations with X heads and N-X tails. So, the probability of X heads is 

   N!/X!/(N-X)! p^X q^(N-X)

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