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Algorithm to compute number ordered selections w/ upper bound restrictions:

• Canonical duplicate: How to find the number of $k$-permutations of $n$ objects with $x$ types, and $r_1, r_2, r_3, \cdots , r_x$ = the number of each type of object?

• My algorithmic approach: permutation of a subset from a set with multiple repetitions

Unordered version:

• Time complexity of number of solutions to equation of varying size, with varying upper-bound range restrictions

Zeilberger quick how-to:https://math.stackexchange.com/a/4322239

How to ask a good question advice: https://math.meta.stackexchange.com/a/34067