Five teams have to compete in a league, with every team playing every other…
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?
Answer: B. 10 — Concept: When n teams play in a round-robin format and every team faces every other team exactly once, one match corresponds to exactly one unique pair of…
- A.
20
- B.
10
- C.
8
- D.
5
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Concept: When n teams play in a round-robin format and every team faces every other team exactly once, one match corresponds to exactly one unique pair of teams. So the total number of matches equals the number of ways to choose 2 teams out of n, i.e., Matches = C(n, 2) = n(n − 1) / 2.
Application:
Here the league has n = 5 teams, so the number of matches equals C(5, 2).
C(5, 2) = 5! / (2! × 3!) = (5 × 4) / (2 × 1).
= 20 / 2 = 10.
Cross-check: Counting from each team's side, every one of the 5 teams plays 4 matches (against the other four), giving 5 × 4 = 20 team-match slots. Since each match is shared between two teams, this count includes every match exactly twice, so the actual number of matches is 20 / 2 = 10 — the same result.
So, 10 matches will have to be held to complete this round of the league.
