Q. In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played? (UPSC Prelims 2010)
Answer: 91
Notes: The number of matches in a round-robin tournament with n teams, where each plays every other once, is given by the combination formula n(n-1)/2. For n = 14, calculate (14 × 13)/2 = 182/2 = 91. This counts each unique pair of teams exactly once, avoiding double-counting. The formula is standard in combinatorics for undirected matches and applies to league tournaments. Option 2 is correct as it matches this result; other options do not fit the formula.