I am struggling with the concept and solving probelms like this. Please help me with the solution and concept for the following problems:

"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 you draw 80 lines on a piece of paper so that no two lines are parallel to each other and no three lines pass through the same point, how many intersections will there be?"

I'm not sure how to approach these problems or what to do. I've heard about some equations but I don't understand how they relate to the problem.