Question

If each of 11 football teams in a college athletic conference played each other team just once in a season, how many games would there be? As part of your answer, make a table like the one in Example 4 on page 7. How many games would there be for 12 teams?

A) 55 games for 11 teams, 66 games for 12 teams
B) 66 games for 11 teams, 78 games for 12 teams
C) 110 games for 11 teams, 132 games for 12 teams
D) 132 games for 11 teams, 144 games for 12 teams

Answer 1

The number of games when 11 football teams play each other once is calculated with the combination formula, resulting in 55 games. For 12 teams, the number of games is 66.

Step-by-step explanation:

To calculate the number of games played when each of 11 football teams in a college athletic conference played each other team just once, we can use the formula for the number of combinations of teams, given by n(n-1)/2, where 'n' is the number of teams. For 11 teams, this calculation would be 11(11-1)/2 or 11(10)/2, which equals 55 games.

When there are 12 teams, the calculation based on the same formula would be 12(12-1)/2 or 12(11)/2, which results in 66 games.

Therefore, the correct answer is A) 55 games for 11 teams, 66 games for 12 teams.