math
posted by mark .
taylor was having a party.she invited 20 friends to her party, if each person shook hands with every other person .how many handshakes would there be? please explain,thanks

21 * 20 = ?

Each of the 20 people will shake hands with 19 other people
20(19)= 380
but that would include duplicates such as A shaking hands with P, and P shaking hands with A, which is the same handshake
so number of handshakes = 20(19)/2 = 380/2 = 190
or
we are choosing pairs from 20
= C(20,2) = 190 
Thanks, Reiny  I goofed and didn't consider that we can't count A and P and P and A.
I included the hostess  so we have 21 people. 
Thanks Ms Sue, and I didn't catch the hostess part, only saw the 20.
So let's go with your answer รท 2 = 21(20)/2 = 210