Find the Number of Games Played in a Round Robin

Essay

Find the number of games played in a round robin tournament for the given numbers of teams. In a round robin tournament every team plays every other team once. $$\begin{array} { r | r } \text { Number of teams } & \text { Number of games played } \\\hline 3 \text { teams } & 3 \text { games } \\4 \text { teams } & 6 \text { games } \\5 \text { teams } & 10 \text { games } \\6 \text { teams } & - \text { games } \\7 \text { teams } & \text { - games }\end{array}$$
Look for a pattern. Find the number of games played in a round robin tournament involving n teams. Find the number of games played in a round robin tournament involving 19 teams.