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Five teams have to complete 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 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 complete in a league, with every team playing every...
1st team play with 2,3,4,5 so total 4 match played
2nd team play with 3,4,5 so total 3 match played
3rd team play with 4,5 so total 2 match played
4th team play with 5 so total 1 match played
so total match played to reach next round is 4+3+2+1=10 is answer
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Five teams have to complete in a league, with every team playing every...
To find the number of matches required to complete the league round, we can use the formula for the number of combinations. In a league round, each team plays against every other team exactly once.
Step 1: Determine the number of teams
In this case, there are five teams in the league.
Step 2: Determine the number of matches between two teams
To find the number of matches between two teams, we can use the formula for combinations. The number of matches between two teams is given by nC2, where n is the number of teams.
nC2 = n! / (2! * (n-2)!)
For this league, the number of matches between two teams is 5C2.
5C2 = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= 10
Step 3: Determine the total number of matches
To find the total number of matches required to complete the league round, we can multiply the number of matches between two teams by the number of combinations.
Total number of matches = Number of matches between two teams * Number of combinations
In this case, the number of matches between two teams is 10, and there are 5 teams in the league.
Total number of matches = 10 * 5
= 50
Therefore, the correct answer is 50 matches. However, the given options do not include this answer. The closest option is 10 matches, which is incorrect.
Step 1: Determine the number of teams
In this case, there are five teams in the league.
Step 2: Determine the number of matches between two teams
To find the number of matches between two teams, we can use the formula for combinations. The number of matches between two teams is given by nC2, where n is the number of teams.
nC2 = n! / (2! * (n-2)!)
For this league, the number of matches between two teams is 5C2.
5C2 = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= 10
Step 3: Determine the total number of matches
To find the total number of matches required to complete the league round, we can multiply the number of matches between two teams by the number of combinations.
Total number of matches = Number of matches between two teams * Number of combinations
In this case, the number of matches between two teams is 10, and there are 5 teams in the league.
Total number of matches = 10 * 5
= 50
Therefore, the correct answer is 50 matches. However, the given options do not include this answer. The closest option is 10 matches, which is incorrect.
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Five teams have to complete 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 complete the league round of matches?a)20b)10c)8d)5Correct answer is option 'B'. Can you explain this answer?
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