Ten (10) teams are playing matches against each other. Assume that each team will play every other team once, how many matches must take place? Write a single number using only digits from 0 to 9 without leading zeroes nor any form of thousands separator.

The number of matches played between 10 teams where each team plays every other team once can be calculated using the combination formula \( \binom{n}{2} \), where \( n \) is the number of teams and \( 2 \) represents the fact that a match involves two teams.

For 10 teams, the number of matches is:

\[
\binom{10}{2} = \frac{10 \times 9}{2} = 45
\]

Thus, the total number of matches is:

**45**

Would you like more details or have any questions?

Here are five related questions:
1. How would the formula change if each team plays every other team twice?
2. What is the general formula for combinations and how does it work?
3. If there were 12 teams, how many matches would take place?
4. How many matches would occur if a knockout tournament was held instead?
5. How does the number of teams affect the total number of matches?

**Tip:** The combination formula \( \binom{n}{2} \) is very useful for calculating pairings in round-robin tournaments.

Discover how to calculate the total number of matches for 10 teams playing a round-robin tournament. Using the combination formula C(n, 2), learn step-by-step how to determine that 45 matches must take place. Suitable for Grades 9-12.

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