Sus King I

A king has $N$ boxes of gold with $N$ gold bars inside each box. However, the king is suspicious of one of his servants. In fact, the servant confided in you that one bar of gold in each box is fake! The king draws out $m$ gold bars from each box and tests if it's real. Let $p(N,m)$ be the probability that the king does not have a fake gold bar in his sample when he draws out $m$ gold bars from each box. For a fixed positive integer $m$, compute $\displaystyle \lim_{N \rightarrow \infty} p(N,m)$. Report the answer with $m = 3$ to the nearest hundredth.