examday

/TMUA

Consider six players $P_1,P_2,P_3,P_4,P_5$, and $P_6$. A team consists of two players (Thus, there are $15$ distinct teams). Two teams play a match exactly once if there is no common player. For example, team $\{P_1,P_2\}$ cannot play with $\{P_2,P_3\}$, but will play with $\{P_4,P_5\}$. Then the total number of possible matches is