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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. ow many matches will have to be held to complete the league round of matches?
- a)20
- b)10
- c)8
- d)5
Correct answer is option 'B'. Can you explain this answer?
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Five teams have to compete in a league, with every team playing every ...
Problem Analysis:
The problem states that there are five teams that need to compete in a league round where each team plays against every other team exactly once. We need to determine the number of matches that will have to be held to complete this league round of matches.
Solution:
To find the number of matches, we can use the combination formula. In a league round, each team will play against every other team exactly once. So, for each team, we need to find the number of matches it will play.
Number of Matches for a Team:
The number of matches for a team can be calculated using the formula n-1, where n is the number of teams. This formula works because each team will play against every other team exactly once, excluding their own team.
So, for a league with five teams, each team will play 4 matches.
Total Number of Matches:
Since there are five teams, we need to calculate the total number of matches by multiplying the number of matches for a team by the number of teams.
Total Matches = Number of Matches for a Team * Number of Teams
Total Matches = 4 * 5 = 20
Therefore, a total of 20 matches will have to be held to complete the league round of matches.
Answer:
The correct answer is option 'A' 20.
The problem states that there are five teams that need to compete in a league round where each team plays against every other team exactly once. We need to determine the number of matches that will have to be held to complete this league round of matches.
Solution:
To find the number of matches, we can use the combination formula. In a league round, each team will play against every other team exactly once. So, for each team, we need to find the number of matches it will play.
Number of Matches for a Team:
The number of matches for a team can be calculated using the formula n-1, where n is the number of teams. This formula works because each team will play against every other team exactly once, excluding their own team.
So, for a league with five teams, each team will play 4 matches.
Total Number of Matches:
Since there are five teams, we need to calculate the total number of matches by multiplying the number of matches for a team by the number of teams.
Total Matches = Number of Matches for a Team * Number of Teams
Total Matches = 4 * 5 = 20
Therefore, a total of 20 matches will have to be held to complete the league round of matches.
Answer:
The correct answer is option 'A' 20.
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