The ABCD football association is considering a Super Ten Football Conference. The top 10 football 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,Oklahoma versus Michigan is the same as Michigan versus Oklahoma.)
A)45
B)50
C)125
D)14

Question

Quizplus · Accepted Answer

This is a combination problem where you need to find how many games can be formed from 10 teams where the order does not matter (since Team A vs Team B is the same as Team B vs Team A). The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items (teams), and k is the number of items to choose (2 for a game). So, C(10, 2) = 10! / [2!(10-2)!] = 45 games.

The ABCD Football Association Is Considering a Super Ten Football