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Most introductory books on probability I have seen open with the combinatorical approach you describe. When it is applicable, this approach is very powerfull. However there is essentially nothing novel in combinatorical probability relative to combinatorics, so research and advanced topics in this field are done under the title of combinatorics, instead of probability. Probability becomes a field in its own right once we move beyond the cases where a combinatorical approach will work.



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