Club Activites Melissa is the activities director for her school's science club and needs to coordinate a "get to know you" activity for the group's first meeting. The activity must last at least 40 minutes but no more than 60 minutes. Melissa has chosen an activity that will require each participant to interact with every other participant in attendance only once and estimates that if her directions are followed, each interaction should take approximately 30 seconds.
a. If n people participate in Melissa's activity, develop a formula to calculate the total number of such interactions that should take place.
b. Prove that the formula found in part a is valid for all positive integral values of n.
c. If 15 people participate, will Melissa's activity meet the guidelines provided to her? Explain.
