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6 votes
6 votes

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 complete the league round of matches?

  1. $20$ 
  2. $10$ 
  3. $8$
  4. $5$
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4 Answers

Best answer
5 votes
5 votes

Answer (B) $10$

We have to select number of ways of choosing $2$ teams out of $5 = {}^5C_2 = 10.$

We can also do like follows:

  • Team 1: Can pick another team in $4$ ways
  • Team 2: Can pick another team (excluding team 1) in $3$ ways
  • Team 3: Can pick other teams in $2$ ways
  • Teams $4$ and $5$ can play in $1$ way
  • So, totally, $4+3+2+1 = 10$ ways.
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7 votes
7 votes
round robin format every team will play 4 matches five teams are there so 5*4 /2 =10 matches
4 votes
4 votes

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

2 votes
2 votes
It can be easily solved using graph theory.

Visualize this problem as a complete graph having $5$ vertices. -> $K_5$

Degree of each vertex = $5*4=20$

So, number of edges = $20/2 = 10$
Answer:

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