Question

How many matches will be played in a league tournament of 10 teams?

• A. 44
• B. 45
• C. 46
• D. 47

Hint:

To calculate the number of matches in a round-robin tournament, use the combination formula: \( \binom{n}{2} \).

Answer 1

The Correct Option is B

Step 1: Understanding the problem.
In a league tournament with 10 teams, each team plays against every other team exactly once. The number of matches can be calculated using the combination formula: \[ \text{Number of matches} = \binom{n}{2} = \frac{n(n-1)}{2} \] where \(n\) is the number of teams. For \(n = 10\), we have: \[ \text{Number of matches} = \frac{10(10-1)}{2} = \frac{10 \times 9}{2} = 45 \]

Step 2: Conclusion.
The correct answer is (B) 45, as 45 matches will be played in the tournament. Final Answer: 45.