Mod note: Removed "Basic calculus" from thread title, as the question doesn't seem to have anything to do with calculus 1. The problem statement, all variables and given/known data Real world kind of thing. Assume I have a set of C components that I want to investigate. I want to give each component a unique identifier. I have N identifiers. What is the probability of having two components with the same identifier (duplicate), given N and C? 2. Relevant equations What I'm looking for! 3. The attempt at a solution So let's say one component gets some identifier. The probability that none of the other components get the same identifier would be: (1- 1/N)C, assuming N>>C (how much bigger would N have to be than C for this to be a valid assumption, btw?) However, by my logic this doesn't yet exclude the possibility that any of the other components have duplicate identifiers to one another. This is where I'm getting stuck. Thanks in advance for any help provided!