Question

Ten members of the Residence Welfare Committee met for their monthly meeting. Each one shakes hands with every other person in the room once? ​

Answer 1

so probability maybe 1/9

Answer 2

Imagine all nine people standing in line. Person number 9 goes down the line shaking each persons hand. That makes eight handshakes so far. Number nine can leave the room, as everybody has now shook his hand.