Poisson Approximation

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.

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$$b \rightarrow p \iff n \gg 1 ~ \& ~ p \ll 1 ~ \& ~ \lambda = np$$

where $b$ is binomial and $p$ is poisson