In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament ?

I. matches of first player with other 5 players II. matches of second player with 4 players other than the first player III. matches of third player with 3 players other than the first player and second player. IV. matches of fourth player with 2 players other than the first player, second player and third player. V. matches of fifth player with 1 player other than the first player, second player, third player and fourth player. So total matches will be 5+4+3+2+1 = 15