Handshaking in Groups
Source: 2012 AIME II Problem 14
March 29, 2012
HMMTAMCaime 2012
Problem Statement
In a group of nine people each person shakes hands with exactly two of the other people from the group. Let N be the number of ways this handshaking can occur. Consider two handshaking arrangements different if and only if at least two people who shake hands under one arrangement do not shake hands under the other arrangement. Find the remainder when N is divided by 1000.