How many handshakes?

This is a blog assignment.

1)  You walk into your first college class and the professor tells you to shake hands and introduce yourself to every other student in the classroom.  Every student shakes hands with every other student exactly once.  How many handshakes were there (there are a total of 10 students in class)?

2)  After everyone finishes shaking hands an eleventh student enters the classroom.  How many handshakes will there be (total) after he is done shaking hands?

3)  What would be the total if there were 20 students in the class?

The following illustration is your hint as to how to figure out these three answers.  Post your three answers on your blog.  Title the post "How Many Handshakes?"

Additional hint-  There is a pattern (formula) to this problem.  Once you figure it out, you can quickly calculate the answer no matter how many people there are.

You may collaborate with your fellow classmates, but you must be able to explain your answers.