# calculation / lower bound of $\sum _{k=0}^d \frac{e^{-\frac{k^2}{2}} \binom{d}{k} \binom{p-d}{d-k}}{\binom{p}{d}}$

Let $$p>d>0$$ be given integers. Is there any trick how I can analytically calculate / simplify the following term:

$$\sum _{k=0}^d \frac{e^{-\frac{k^2}{2}} \binom{d}{k} \binom{p-d}{d-k}}{\binom{p}{d}}$$

Edit: Since this seems impossible I'm looking for a lower bound

• Somehow seems unlike. The $e^{-k^2}$ is really problematic. May 14 at 0:53