On a combinatorial problem in the Secret Santa ritual

11 Mar 2020 Steinicke Alexander Penz Markus Penz Bine

The Secret Santa ritual, where in a group of people every member presents a gift to a randomly assigned partner, poses a combinatorial problem when considering the probabilities involved in the formation of pairs, where two persons exchange gifts mutually. We give different possible derivations for such probabilities by counting fixed-point-free permutations with certain numbers of 2-cycles...

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