In a chess tournament, each player plays every other player exactly once. If the

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Question: In a chess tournament, each player plays every other player exactly once. If there are 10 players, how many games are played?

Options:

Correct Answer: 45

Solution:

The number of games played is given by n(n-1)/2. For 10 players, it is 10(10-1)/2 = 45.

In a chess tournament, each player plays every other player exactly once. If there are 10 players, how many games are played?

In a chess tournament, each player plays every other player exactly once. If there are 10 players, how many games are played?

Step 1: Understand that each player plays against every other player exactly once.
Step 2: If there are 10 players, we need to find out how many unique pairs of players can be formed.
Step 3: The formula to find the number of unique pairs from n players is n(n-1)/2.
Step 4: Substitute the number of players (n = 10) into the formula: 10(10-1)/2.
Step 5: Calculate (10-1) which is 9.
Step 6: Multiply 10 by 9 to get 90.
Step 7: Divide 90 by 2 to get 45.
Step 8: Therefore, the total number of games played is 45.

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 players.
Formula Application – It assesses the ability to apply the formula for combinations, n(n-1)/2, to find the total number of games played in a round-robin tournament.