Use any member of a string union in a template literal at most once

I have a union of 3 possible strings:

type AllowedWords = "one" | "two" | "three";

I want to create a template literal type that allows any of those 3 words in any order, but each member should only be included up to once. For example, this should be an exhaustive list of all possible matches:

• one
• two
• three
• onetwo
• onethree
• twoone
• twothree
• threeone
• threetwo
• onetwothree
• onethreetwo
• twoonethree
• twothreeone
• threeonetwo
• threetwoone

How can I define a type that represents that?