2022 SSMO Accuracy Round Problems/Problem 1

Problem

Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) $f:S\rightarrow S,$ where $S=\{1, 2, 3, 4, 5\}$ . What is the average of $f(1) + f(2) + f(3)$ , over all $f$ ?

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2022 SSMO Accuracy Round Problems/Problem 1

Problem

Solution