Let's say we have a deck of 52 index cards each labeled with a distinct number from one to fifty-two on one side and left blank on the other side. We shuffle the deck at least eight times. What is the probability we do not select an index card that has been labeled one without replacement by the 52nd selection?

Of course, we expect the answer to be zero or have a zero probability. In practice, the answer is [tex](\frac{1}{52})^{52} \approx 5.859 * 10^{-90}[/tex] which is clearly not zero.

However, if we have an infinite deck of index cards labeled from one to infinity, then we approach a zero probability for selecting that index card labeled one by the infinite selection... Right?