If we are in a room of five people we can determine the number of handshakes by this line of reasoning: the first person will shake his own hand of the first person they already shook, the third person will shake two hands same reasoning the fourth person will shake 1 hand that of the fifth person. the fifth person will shake 0 hands. so there will be a total of 1+2+3+4= 10 handshakes. determine the number of handshakes, h, that will occur for each number of people , n, in a particular room