Directions: Carry One Mark Each.

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches?

Let's assume that the 5 teams are (A), (B), (C), (D) and (E). From team (A), playing with (B), (C), (D) and (E) teams, there are 4 matches. For team (B), it will play with (C), (D) and (E) teams because with (A), it has already played. So, there are 3 matches. As from team (C), 2 matches. As from team (D), 1 match. Total matches played in the league = 4 + 3 + 2 + 1 = 10 matches Numbers of matches = number of ways to select two teams = 5c₂ = 10