In a league format, if each team plays 3 matches against every other team and th
Practice Questions
Q1
In a league format, if each team plays 3 matches against every other team and there are 4 teams, how many matches are played in total?
12
6
8
9
Questions & Step-by-Step Solutions
In a league format, if each team plays 3 matches against every other team and there are 4 teams, how many matches are played in total?
Step 1: Identify the number of teams. There are 4 teams.
Step 2: Determine how many matches each team plays against every other team. Each team plays 3 matches against each of the other teams.
Step 3: Calculate how many other teams each team plays against. Since there are 4 teams, each team plays against 3 other teams.
Step 4: Calculate the total number of matches played by one team. One team plays 3 matches against each of the 3 other teams, so that is 3 matches * 3 teams = 9 matches.
Step 5: Since each match involves 2 teams, we need to avoid double counting. To find the unique matches, we divide the total matches by 2. So, 9 matches / 2 = 4.5, but since we are counting matches, we will consider the unique pairs of teams.
Step 6: Calculate the number of unique pairs of teams. The number of unique pairs of 4 teams is given by the formula n(n-1)/2, where n is the number of teams. So, 4(4-1)/2 = 4 * 3 / 2 = 6 unique pairs.
Step 7: Since each unique pair of teams plays 3 matches, multiply the number of unique pairs by 3. So, 6 unique pairs * 3 matches = 18 total matches.
