Challenge Question 6/28/10 - Mundane Goblet

[marc.gagnon]

Can you help me understand what the 2 and the 4 represent in the cobinatorics denominator.


In the Mundane Goblet competition, 6 teams compete in a "round robin" format: that is, each team plays every other team exactly once. A team gets 3 points for a win, 1 point for a tie (a draw), and 0 points for a loss. What is the difference between the maximum total points and the minimum total points that can be gained by all teams (added together) in the Mundane Goblet competition

Explanation provided:

First, we should determine the number of games played in this competition. We can count them in at least 2 different ways:
Method (1) Brute Force
Method (2) Combinatorics. We have a pool of 6 teams, and we want to count how many different pairs of teams (to play a game) we can select, without caring about order. Using either the anagram method or the formula for combinations, we get 6!/(2!4!) = 15 games

[george.kourdin]

combiantions formula is nCr or n!/ r!(n-r)!

we want to figure out how many possible pair arrangements (2 teams playing each other) we can get from a pool of 6 teams. we don't care exactly how these teams are going to be arranged, we are just trying to figure out some n number of arrangements from a population of 6 teams.

n=6 = our population
r = 2 = our pair or group of 2
n-r = 4

[marc.gagnon]

Thanks!

[jnelson0612]

Great! :-)