Lets start with the generic item (d). In order to draw a chord we need to pick two endpoints from the total of n points of the circle and draw the line between them. The total amount of lines we can draw is equivalent to the total pair of points we can pick to draw them.
In other words, we can draw as many chords as the amount of subsets of 2 elements we can pick from a set of n. That number is the combinatorialnumber of n with 2 given by
B) calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment
E) taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch