Consideration is being given to forming a Super Ten Basketball Conference. The top 10 university basketball teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, McMaster versus Alberta is the same as Alberta versus McMaster.)
A) 45
B) 50
C) 125
D) 14

Question

Quizplus · Accepted Answer

The total number of games can be calculated using the formula for combinations since each game is between two teams and the order does not matter. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of teams and k is the number of teams in each game (2 in this case). So, for 10 teams, it would be C(10, 2) = 10! / [2!(10-2)!] = 45 games.

Consideration Is Being Given to Forming a Super Ten Basketball