In a league (round-robin) football tournament, every team plays every other team exactly once.
a. (i) Prove that a tournament involving n teams requires 2n(n−1) matches.
b. (ii) Using your result from part (i), find the number of matches that must be scheduled when there are 15 teams.
c. (iii) The 15-team tournament is to be completed in 5 days with the same number of matches played each day. How many matches should be scheduled per day?