A derangement is a permutation in which no element appears in its 'natural' position; the number of derangements of n distinct items is D(n) = n! x sum_{k=0}^{n}((-1)^k/k!), and D(3) = 2.
Placing 3 differently-colored balls into 3 differently-colored boxes such that no ball goes into the box of its own color is exactly the derangement problem...
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