In a classroom, there is 31 people. If everyone shakes everyone else's hand once, then how many total handshakes happened?
The formula for number of handshakes is n(n-1)/2 where n is the number of people. Plug 31 for n into the equation.
n(n-1)/2
=31(31-1)/2
=31(30)/2
= 465 handshakes
31 people have to shake hands with 30 other people
31 * 30 = 930 BUT each handshake involves TWO people , so divide that number by 2 = 465 handshakes ( as gs found below)