In a round-robin tournament, each team plays every other team exactly once. If t

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Question: In a round-robin tournament, each team plays every other team exactly once. If there are 10 teams, how many games will be played?

Options:

Correct Answer: 45

Solution:

The number of games is given by n(n-1)/2, which for 10 teams is 10(9)/2 = 45.

In a round-robin tournament, each team plays every other team exactly once. If there are 10 teams, how many games will be played?

In a round-robin tournament, each team plays every other team exactly once. If there are 10 teams, how many games will be played?

Step 1: Understand that in a round-robin tournament, each team plays every other team exactly once.
Step 2: Identify the number of teams, which is 10 in this case.
Step 3: Use the formula for calculating the number of games, which is n(n-1)/2, where n is the number of teams.
Step 4: Substitute the number of teams (10) into the formula: 10(10-1)/2.
Step 5: Calculate 10-1, which equals 9.
Step 6: Multiply 10 by 9, which equals 90.
Step 7: Divide 90 by 2, which equals 45.
Step 8: Conclude that there will be 45 games played in total.

Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of unique pairs (games) that can be formed from a set of teams.
Round-Robin Format – Understanding the structure of a round-robin tournament where each team competes against every other team exactly once.