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?
A. 20 B. 10 C. 8 D. 5
GATE 2015 · General Aptitude · Combinatorics · medium
Answer: 10 matches (option B)
Apply round-robin match formula: With n = 5 teams and each pair playing once: C(5,2) = 5*4/2 = 10.
Verify via each team's match count: Each team plays 4 matches. Total team-appearances = 5 * 4 = 20. Each match has 2 teams, so matches = 20/2 = 10.