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The problem presented in the image asks how many matches are played in a football tournament where each team plays against every other team exactly once. The total number of teams participating is 567.

This is a classic problem of combinations where we need to calculate the number of ways to choose 2 teams out of 567 to play a match. The formula to calculate the number of matches is given by:

\[
\text{Number of matches} = \binom{n}{2} = \frac{n(n-1)}{2}
\]

Where \( n \) is the total number of teams.

Given:
\[
n = 567
\]

Let's calculate the number of matches.

\[
\text{Number of matches} = \frac{567 \times (567 - 1)}{2} = \frac{567 \times 566}{2}
\]

Now, I'll calculate this.The total number of matches played in the tournament, where each of the 567 teams plays against every other team exactly once, is **160,461**.

Would you like any further details or have any questions? Here are some related questions to expand on this topic:

1. How would the number of matches change if there were 100 more teams?
2. If each match lasted 90 minutes, how many total hours would be spent playing all the matches?
3. What if each team played every other team twice (home and away)? How would the number of matches change?
4. How can this formula be applied to other types of tournaments, like round-robin or knockout tournaments?
5. How many matches would be played if there were only 10 teams?

**Tip:** Understanding combinatorial mathematics is essential for solving problems involving pairings or groupings, such as in tournaments and scheduling.

567 times participam de um campeonato de futebol. Cada time joga contra outro time exatamente uma vez. Quantas partidas são jogadas no total?

Learn how to calculate the total number of matches in a football tournament with 567 teams where each team plays against every other team exactly once. This problem uses combinatorial mathematics and is suitable for students in Grades 9-12.

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