In a round-robin format tournament with 8 teams, each team plays every other tea

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Question: In a round-robin format tournament with 8 teams, each team plays every other team once. How many matches are played in total?

Options:

Correct Answer: 28

Solution:

The total number of matches is calculated using the formula n(n-1)/2, where n is the number of teams. Here, 8(8-1)/2 = 28.

In a round-robin format tournament with 8 teams, each team plays every other team once. How many matches are played in total?

In a round-robin format tournament with 8 teams, each team plays every other team once. How many matches are played in total?

Step 1: Identify the number of teams in the tournament. In this case, there are 8 teams.
Step 2: Understand that in a round-robin format, each team plays every other team exactly once.
Step 3: Use the formula to calculate the total number of matches: n(n-1)/2, where n is the number of teams.
Step 4: Substitute the number of teams into the formula: 8(8-1)/2.
Step 5: Calculate (8-1) which equals 7.
Step 6: Multiply 8 by 7 to get 56.
Step 7: Divide 56 by 2 to find the total number of matches: 56/2 = 28.
Step 8: Conclude that the total number of matches played in the tournament is 28.

Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of unique matches in a round-robin tournament format.
Mathematical Formula Application – It assesses the ability to apply the formula for combinations, n(n-1)/2, to find the total number of matches played.