I notice that the function $\binom{C}{x}$, where $C$ is some constant, resembles a Gaussian function; for example, here is the plot for $\binom{20}{x}$:
This corresponds to the Gaussian function $a e^{- { \frac{(x-b)^2 }{ 2 c^2} } }$, where $a$ is $\binom{20}{10}$, $b$ is 10, and $c$ (determined through curve fitting) is ~2.2689.
$\binom{20}{x}$ corresponds to $\frac{20!}{x!(20-x)!}$; how is this related to a Gaussian function?