How to calculate probability of viewing redundant requirements

Hi! I was presented with an interesting study today which showed some rather unbelievable results and I would like to calculate a probability to investigate my suspicion. However it has been a while since I did any in depth prob & stats so I'm hoping someone can help me.

Basically, say there are 500 engineering requirements in a database. If 2/5 of these requirements are duplicates, I'd like to calculate the probability that if a person started reading requirements at random, without repeating any, what is the probability after reviewing X requirements that at least on pair of duplicates were read.

As an example, say I start going through the requirements and after reading X, what is the probability I have pulled and read any redundant pair?

As an extended generalization, what would the equation be if I knew that 2/5 were redundant and of those 1/5 were triplicates? Here I'm interested in the probability of viewing at least two of the same requirement.
I'm also relearning the application of stats and this problem relates to another problem I found about people in a group having the same birthday at 50% chance and it was a surprisingly small number, 23. In your problem, the efficient approach may to calculate the complement or how many requirements can be read all being unique where M (number of requirements read) is greater than or equal to 2. The equation is 1 - 500! / 500M (500 - M). As M increases the probability of reading a duplicate pair increases until there is 40% chance of having a pair at M.