How many handshakes all together?

There are 45 people at a party. If each person shakes hands with every person,how many handshakes will there be all together?Suppose there are n people at the party. How many handshakes will there be in terms of n? How many handshakes does each person make? How many handshakes would there be if there were smaller groups of people?Are there any patterns? Please answer all questions and show all of the work.