Hi shasadou,
This question can be answered in a couple of different ways. If you know the Combination Formula, then you can use that...
N!/[K!(N-K)!] where N is the total number of Teams and K is the Subgroup.
In this prompt, N = 16 and K = 2...
16!/[2!(14!)] =
(16)(15)/(2)(1) =
120 different games played
You can also use 'brute force' and a bit of logic to answer the question....
Let's call the teams...ABCDE FGHIJ KLMNO P
Team A plays each of the other 15 teams, so that's 15 games.
Team B already played Team A, so it plays 14 OTHER games.
Team C already played Teams A and B, so it plays 13 OTHER games.
Team D already played Teams A, B and C, so it plays 12 OTHER games.
Etc.
The sum of all of these games is...
15+14+13.....+3+2+1 = 120
Final Answer:
GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
Co-Founder & GMAT Assassin
Special Offer:
Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/