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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 complete the league round of matches?

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

1 comment

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.
by

How many matches will have to be held to complete the league round of matches?

I interpreted this line as total number of matches to be palyed in the whole tournament....it gives 5C2 + 4C2 + 3C2 + 2C2 = 10 + 6 + 3 + 1 = 20..

In Many questions interpretation is more tricky then actually solving the question..

@Nitesh Methani

Also given,

every team playing every other team exactly once.

So 10 will be the answer.

round robin format every team will play 4 matches five teams are there so 5*4 /2 =10 matches

1 comment

Sir please explain how to implement

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

by
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 = $20/2 = 10$