Four matches are to be played in a chess tournament. In how many ways can result be decided?
Question
Four matches are to be played in a chess tournament. In how many ways can result be decided?
Solution
To determine the number of ways the results of four matches can be decided in a chess tournament, we can break down the problem as follows:
1. Break Down the Problem
Each match can end in one of three outcomes: Player A wins, Player B wins, or the match ends in a draw. Therefore, for each of the four matches, there are three potential outcomes.
2. Relevant Concepts
The total number of possible outcomes for multiple matches can be calculated using the formula:
In this case, the number of outcomes per match is 3 (win for A, win for B, or draw), and the number of matches is 4.
3. Analysis and Detail
Using the formula:
Calculating :
4. Verify and Summarize
We calculated the total number of outcomes by considering each match independently. Each match has 3 outcomes, and there are 4 matches, leading to a total of different ways the results can be decided.
Final Answer
The total number of ways the results of the four matches can be decided is .
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