1) If there is 10 people in the room then there will be 45 handshakes because the first person shakes hands with everyone and that gives you 9 handshakes then that person sits down and that person shakes hands with everyone so there would be eight handshakes. So everyone keeps repeating the process they shake hands with everyone still standing and every time they do the number of handshakes goes down one because after each person shakes everyone's hand they sit and they don't have to shake hands anymore.
2) The answer is 55 if there is 11 people in the class because if there is one person added to the group they have to shake hands with everyone once which would lead to ten handshakes and you add the 10 to the 45 that you had when there was 10 people and you get 55.
3)If there is 20 people in the class then there will be 190 handshakes because you just keep repeating the process and adding ten more people to the class gives you 190 different handshakes.
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