There are 6 pairs (12 people) and they must be divided into 3 teams. All teams must have 1 or more occupants. Both people from a pair must not be in the same team.

I already answered a similar question, the only difference was that there were two teams instead of three. If x is the number of pairs, I found the no. of ways to divide the pairs into 2 teams such that no pairs are in the same team, f(x), to be equal to the sum of (x-1) choose n from n=0 and n=(x-1). Another way of writing f(x) is f(x)=2^(x-1).

Please correct me if I made a mistake, because chances are I did! I'm new to combinatorics and don't know a whole lot, but I really need an answer to this question