Pairs, in this case, relates to a group of 2 or more. We have 6 friends. Let's call them A,B,C,D,E,F. This will allow us to make a [some sort of] combination tree:
1. ABC against DEF
2. ABD against CEF
3. ABE against CDF
4. ABF against CDE
5. ACD against BFE
6. ACE against BDF
7. ACF against BDE
8. ADE against BCF
9. ADF against BCE
10. AEF against BCD
I believe there are 12 combinations... I just can't think of the last 2 though.