First Repeat in the Cereal Boxes

Each cereal box holds one of $n$ distinct figurines, uniform and independent across boxes. Buy $k$ boxes, where $n \to \infty$ with $k/\sqrt{n} \to c$. Let $Z$ be the number of wasted boxes: $k$ minus the number of distinct figurines collected.

$Z$ has a limiting distribution. Taking $c = 2$, what is $P(Z \geq 1)$, the limiting probability that at least one figurine arrives twice?

Answer format: round to 3 decimal places.