$\binom{n}{k} (K/N)^k (1-K/N)^{n-k}$

$\frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}$

$\frac{\binom{n}{k} \binom{N-n}{K-k}}{\binom{N}{K}}$

$\frac{e^{-\lambda} \lambda^k}{k!}$ where $\lambda = nK/N$