E – 3039 Permutations & Combinations for Samples with Limited Repetitions

This Python script addresses a fundamental problem in combinatorics: calculating the number of distinct permutations and combinations for a multiset (a set with duplicate elements). The trial is to determine how many ways we can select and arrange m items from a collection where individual elements have limited available quantities. A classic example is finding all possible 2-letter words from the letters in “aaabbbbc”. The script efficiently solves this by leveraging the mathematical principles of generating functions and the itertools module to iterate through all possible selection scenarios, validating them against the constraints, and applying combinatorial formulas to count the valid outcomes.