Combinatorics: do you really know how to count?
Counting sounds simple—until you need to be certain you’ve counted everything exactly once. Today I’ve uploaded a three-part series, Combinatorics: Do You Really Know How to COUNT!?
In Part 1, I work through the core ideas: the multiplication principle, permutations, combinations, and arrangements with repeated objects—not just the formulas, but why they work and when dividing out duplicates can go wrong.
In Part 2, we put those principles to work on four TMUA-style questions: race results, coefficients in an expansion, dice probabilities and counting functions where .
And in a short bonus video, we finish with one more problem, solved in two ways: using flexible variables, and then a proper proof.
Throughout, two questions guide us: have we counted every possibility, and have we counted anything more than once?
Watch Part 1 · Watch Part 2 · Watch the bonus · Browse all videos