Constructive counting is counting the number of integers, lists, etc., that satisfy a certain property by "constructing" it. This strategy is useful for complicated counting or combinatorics questions, as the problem can be broken down into cases, the number of possibilities in each case can be computed, and those numbers can be summed to find the final answer.
This video is a great introduction to permutations, combinations, and constructive counting: https://www.youtube.com/watch?v=t6a4uHEwQnM&t=1868s
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