You are looking for Composition_(combinatorics) and need to filter on the number of parts (after taking away 1 postcard for each pidgeon hole as suggested below). I have not found any code on CPAN for this. The bad news is that there are exponentially many compositions for a given number of postcards.

In reply to Re^3: Combinatorics problem. by hdb
in thread Combinatorics problem. (Updated with more info.) by BrowserUk

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