If a football tournament has 16 teams and each team plays every other team once,

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Question: If a football tournament has 16 teams and each team plays every other team once, how many matches are played in total?

Options:

Correct Answer: 120

Solution:

The total number of matches is calculated using the formula n(n-1)/2, where n is the number of teams. Here, it is 16(15)/2 = 120.

If a football tournament has 16 teams and each team plays every other team once, how many matches are played in total?

If a football tournament has 16 teams and 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 16 teams.
Step 2: Understand that each team plays every other team once. This means we need to find out how many unique pairs of teams can be formed.
Step 3: Use the formula for calculating the number of matches, which is n(n-1)/2. Here, n is the number of teams.
Step 4: Substitute the number of teams into the formula: 16(16-1)/2.
Step 5: Calculate 16-1, which equals 15.
Step 6: Multiply 16 by 15, which equals 240.
Step 7: Divide 240 by 2 to find the total number of matches: 240/2 = 120.
Step 8: Conclude that the total number of matches played in the tournament is 120.

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.