Explanation

This is the classic ‘handshakes’ counting problem: each match involves two players, and every pair of players meets exactly once. With 6 players, the first player has 5 opponents, the second has 4 new opponents (having already played the first), and so on — 5 + 4 + 3 + 2 + 1 = 15. Equivalently, the number of ways to choose 2 players out of 6 is C(6,2) = 6×5/2 = 15. A common mistake is to count 6 × 5 = 30, which counts every match twice (A-vs-B and B-vs-A are the same fixture); options C (20) and D (25) have no combinatorial basis, and A (10) is too small. Hence 15 matches are played, option B.