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Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to completer the league round of matches?
- a)20
- b)10
- c)8
- d)5
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Five teams have to compete in a league, with every team playing every ...
Understanding the Problem
In a league where every team plays every other team exactly once, we can calculate the total number of matches by understanding the combinations of teams that can compete against each other.
Number of Teams
- We have 5 teams in total.
Calculating Matches
- Each match involves 2 teams.
- The number of ways to choose 2 teams from 5 can be calculated using the combination formula, which is given by:
C(n, r) = n! / [r!(n-r)!]
- Here, n = 5 (total teams) and r = 2 (teams in each match).
Applying the Formula
- Using the formula, we calculate:
C(5, 2) = 5! / [2!(5-2)!] = (5 × 4) / (2 × 1) = 20 / 2 = 10.
Conclusion
- Therefore, a total of 10 matches will be held in the league round.
Final Answer
- The correct answer is option 'B' (10 matches).
This method ensures that each team plays against every other team exactly once, resulting in a fair and balanced competition.
In a league where every team plays every other team exactly once, we can calculate the total number of matches by understanding the combinations of teams that can compete against each other.
Number of Teams
- We have 5 teams in total.
Calculating Matches
- Each match involves 2 teams.
- The number of ways to choose 2 teams from 5 can be calculated using the combination formula, which is given by:
C(n, r) = n! / [r!(n-r)!]
- Here, n = 5 (total teams) and r = 2 (teams in each match).
Applying the Formula
- Using the formula, we calculate:
C(5, 2) = 5! / [2!(5-2)!] = (5 × 4) / (2 × 1) = 20 / 2 = 10.
Conclusion
- Therefore, a total of 10 matches will be held in the league round.
Final Answer
- The correct answer is option 'B' (10 matches).
This method ensures that each team plays against every other team exactly once, resulting in a fair and balanced competition.
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Community Answer
Five teams have to compete in a league, with every team playing every ...
We need to make the all possible pairs of two teams from 5 without worrying about their order. Means we need to find 5C2.( combinations).
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