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To what extent are the Inclusion Exclusion principle and Generating Functions interchangeable? Is there a general principle? For instance, I asked the following question, Number of 5 letter words over a 4 letter group using each letter at least once. Could it be solved with generating functions?

In general, what classes of problems solvable by inclusion exclusion are solvable by generating functions?

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    Most problems solved with generating functions have no relation to inclusion-exclution. A few problems that are naturally solved by inclusion-exclusion may instead by solved using generating function. So: NO, they are not interchangeable.2012-02-13
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    So what types / classes of Inclusion - Exclusion problems lend themselves to generating functions?2012-02-13

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