In a webcomic I'm reading, there are twelve trolls on another planet that form lots of relationships with each other. A given troll can form a relationship with any other troll. One of the trolls, Nepeta, keeps a chart of relationships between the beings (including herself). There can be up to \(6\) pairings between the trolls at any given time, but there can be less; a troll is not necessarily in a relationship. If a troll can be in at most \(1\) relationship at a time, How many different charts can Nepeta make?
Please give your answer along with the math behind it. I really feel that I should know how to do this, but the exact method escapes me. Thanks!