Eight members of a chess club are having a tournament. In the first round every player will play a chess game against every other player. How many games will be in the first tournament

Same as handshake problem.

Each of n persons plays against n-1 persons for a total of n (n-1) / 2 games.

The division by 2 is necessary to avoid double counting the game A vs B and B vs A.

For n=8, then number of games played in the first round is 8 (8-1) / 2=28 games.