How many handshakes

If there was 10 students the total of hand shakes are 45 and if one more comes along it will be 55 handshakes.
If there was 20 twenty students it would be 191 handshakes.

This is why, if you were to add people and multiply then there is going to be repeated handshakes.
Like the 10 people did a total of 45, but one more came along. All you have to do is add the last person before he starts to shake hands. So number 10 was the last person to shake hands so add 45 to 10 and you receive 55.  if another person walks in you add 55+11= 66. That's the way it goes through.