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Here is the problem I'm faced with, as best as I can describe it.

There is a set of 256 values (a byte), and 108 values are chosen from this set. Each choice may be any value from 0 to 255. What is the probability that once the values are chosen, there will be six distinct pairs of duplicate values, and all other 96 values will be unique?

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    What's the relevance of having 256 values to pick from? Without knowing what they are I don't see what the question is really asking. Unless you're saying that you're generating 108 uniformly distributed integers between 0 and 255 inclusive, in which case this should be worded more clearly.2012-06-20
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    Are all $256^{108}$ choices equally likely?2012-06-20
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    Sorry, you're right in phrasing that I'm generating 108 uniformly distributed integers between 0 and 255 inclusive.2012-06-20
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    Just out of curiosity, did you change the question shortly after positing it or am I going mad?2012-06-20

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