15 tennis players take part in a tournament. Every player plays twice with…

The number of distinct games between different pairs of players in a round-robin format is given by the combination formula C(n, 2) = n(n-1)/2, which counts how many ways 2 players can be chosen out of n. When every pair meets more than once, the total number of games is this count of pairs multiplied by how many times each pair plays.

1. There are 15 players, so the number of distinct pairs of players is C(15, 2) = (15 x 14) / 2.

2. Evaluating this gives C(15, 2) = 105 distinct pairs of players.

3. Since every pair of opponents plays twice (not once), multiply the number of pairs by 2: 105 x 2.

4. This gives a total of 210 games.

Cross-check: each of the 15 players faces 14 different opponents, twice each, giving 28 matches per player. Summing over all 15 players counts every match twice (once from each side), so the total is (15 x 28) / 2 = 210, confirming the result.