Ques: There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played? A. 15 B. 16 C. 28 D. 56 E. 64 There are three methods to solve such ques. 1st) The total # of games played would be equal to the # of different pairs possible from 8 teams, which is C 2 8 = 28 C 8 2 = 28 . Formula will be n!/(n-r)!*r! = 8 ! 2 ! 6 ! = 4 ∗ 7 = 28 The answer here is the combination 8C2 ( 8 teams C hoose 2 ) which mean \frac{8!}{6!x2!} --> \frac{8x7}{2} To understand that we just have to think that each of the 8 team plays against 7 other (8x7) but they play each team exactly once so we divide the total by 2. We divide by 2 because "TEAM A VS TEAM B" is the same as "TEAM B VS TEAM A" So we end up with \frac{8x7}{2}= 28 If there are n teams need to play exactly once , then they play with (n-...