OG - PS - #121

by **slsu** Mon Sep 17, 2007 11:24 pm

Question: There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

(A) 15
(B) 16
(C) 28
(D) 56
(E) 64

Answer: (C)

While the OG explanation seems pretty straightforward, I was hoping that an explanation could be offered using MGMAT's Line Method.

Thank you!

by **StaceyKoprince** Mon Sep 24, 2007 9:46 pm

I assume by Line Method you mean the Anagram Grid? You could probably find a way to make it work, but that method is meant to replace the two main math formulas for combinations and permutations. The above question can be answered using the Fundamental Principle of Counting, which is a "lower" concept than comb / perm. (You'll notice that OG doesn't use the factorial formulas to solve this one.) So it's actually simpler not to use the anagram method here.

Fundamental Principle of Counting tells us: 8 teams play 7 other teams (8*7), but each game is played by two teams, so to count up the number of games, divide by 2. (8*7)/2 = 28.