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In a round-robin tournament, each player plays against every other player exactl

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Question: In a round-robin tournament, each player plays against every other player exactly once. If there are 10 players, how many matches will be played?

Options:

  1. 45
  2. 90
  3. 50
  4. 100

Correct Answer: 45

Solution: 

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

In a round-robin tournament, each player plays against every other player exactl

Practice Questions

Q1
In a round-robin tournament, each player plays against every other player exactly once. If there are 10 players, how many matches will be played?
  1. 45
  2. 90
  3. 50
  4. 100

Questions & Step-by-Step Solutions

In a round-robin tournament, each player plays against every other player exactly once. If there are 10 players, how many matches will be played?
  • Step 1: Understand that in a round-robin tournament, each player plays against every other player exactly once.
  • Step 2: Identify the number of players, which is 10 in this case.
  • Step 3: Use the formula for calculating the number of matches, which is n(n-1)/2, where n is the number of players.
  • Step 4: Substitute the number of players into the formula: n = 10, so we calculate 10(10-1)/2.
  • Step 5: Simplify the calculation: 10(9)/2.
  • Step 6: Multiply 10 by 9 to get 90.
  • Step 7: Divide 90 by 2 to get 45.
  • Step 8: Conclude that there will be 45 matches played in total.
  • Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of unique pairs (matches) that can be formed from a set of players.
  • Round-Robin Tournament Structure – It assesses knowledge of the round-robin format where each participant competes against every other participant exactly once.
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