Combinatorics · Digit sums · Digit products · Equinumerous sets · Compositions
Let \(n\) be a positive integer. Let \(A_n\) be the set of all \(n\)-digit numbers whose decimal digits add up to \(4\), and let \(B_n\) be the set of all \(n\)-digit numbers whose decimal digits multiply to \(8\). For each \(n\), determine which of the two sets has more elements.
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Serbian Regional Competition (Okruzno takmicenje) 2022, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source