Twelve people form a circle.

12 people are standing in a circle. Each person will randomly point to another person, with no bias in the pointing direction except that they'll always point to a person rather than empty space. No one can point to oneself, but multiple people can point to the same person.

What's the probability that there will be at least 3 pairs of people who are both pointing at each other? (Example: Alice points at Bob while Bob points at Alice. That's a pair of people pointing at each other.)

You should get an answer rounding to .007111