$\binom{n}{k} (\frac{\lambda}{\lambda+\mu})^k (\frac{\mu}{\lambda+\mu})^{n-k}$

$\binom{n}{k} (\frac{\lambda+\mu}{\lambda})^k (\frac{\lambda+\mu}{\mu})^{n-k}$

$\frac{e^{-(\lambda+\mu)}(\lambda+\mu)^n}{n!}$

$\frac{\lambda^k e^{-\lambda}}{k!} \times \frac{\mu^{n-k} e^{-\mu}}{(n-k)!}$