Now some number n of schools are going to send their baseball teams to a tournament, and each team must play each other team exactly once. Let us think of the teams as numbered 1 through n. (a) How many games does team 1 have to play in? (b) How many games, other than the one with team 1, does team two have to play in? (c) How many games, other than those with the first i 1 teams, does team i have to play in? (d) In terms of your answers to the previous parts of this problem, what is the total number of games ? Write your answer as a sum of numbers and explain your answer using the sum principle. (e) (not for credit but for fun) Do you know what the sum in the previous part adds up to? If you do you can write it up, if not, you can experiment with small values of n and guess the answer.