Fixed-point-free Permutations: Secret Santa
Secret Santa is a Western Christmas tradition
in which members of a group or community
are randomly assigned a person
to whom they give a gift.
(The identity of the gift giver remains secret.)
This is a typical example for a permutation (the gifts are permuted).
Remember: not all permutations are fixed-point-free!
and this is nearly independent of the size of the group
The probability that someone gets back the own gift, is around 63 %,
(even if all people from Shanghai would play the game).