Poisson Approximation
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$P (\lambda) = {{e^{-\lambda} \lambda^x} \over x!}$
$b \rightarrow^d p$ if $n >> 1$, $p << 1$ and $\lambda = np$
In Probability,
$$ {n \choose x} = {n! \over x! (n-x)!} $$
$$ b(n, p) = \text{Poisson}(\lambda) ~ \text{where} ~ \lambda = np $$
$$ n \gg 1 ~\text{and} ~ p \ll 1 $$
approximates binomial distribution.
$$ b \rightarrow p \iff n \gg 1 ~ & ~ p \ll 1 ~ & ~ \lambda = np $$
where $b$ is binomial and $p$ is poisson