# Basic probability: chance of observing sets from draws w/wo replacement

As will be evident from the question I am a complete novice in probability. I am trying to figure out which probability domain I need to look for in questions as: If one have a finite number of the labels, say 100 different ones then what will be the probability of drawing a certain set of labels (the order does not matter) given D draws. I suspect that if you have infinite copies of each label it is like drawing and putting the label back into the pool. For instance how would one start to answer:

1. What is the chance of getting two similar labels from eight draws.
2. Extend that to, say, 3 times 3 similar labels and 5 times 2 similar labels from 1000 draws.
3. What is the probabilities for the above two questions if you only have 100 copies of each label (and thus no replacement)

I would happily appreciate suggestions to further online reading of what I know is very basic probability theory.