Help solve the math promblems

23. The twelfth grade class of 80 students is assembled in a large circle on the football 24. 25. 26. 27. field at halftime. Each student is connected by a string to each of the other class members. How many pieces of string are necessary to connect each student to all the others? (1) If you draw 80 lines on a piece of paper so that no 2 lines are parallel to each other and no 3 lines pass through the same point, how many intersections will there be? If there are 20 couples at a party, how many different handshakes can there be between pairs of people? Assume that the two people in each couple do not shake hands with each other. If a polygon has 24 sides, how many diagonals are there from each vertex? How many diagonals are there in all? If a polygon has a total of 560 diagonals, how many vertices does it have? @