At a teacher’s conference on the first Saturday in November in Palm Springs, CA, 100

Question

teachers meet in a large room. Each teacher shakes the hand of every teacher in the
room, except for his or her own hand. How many total handshakes were made?

Answer 1

Simply C(100,2) = 100!/(98!2!) = 4950

(each of the 100 person shakes hands with 99 others,
that would give us 9900 handshakes.
But that would include duplications of the kind
A vs B and B vs A, which would be the same handshake,
so we have to divdide the 9900 by 2 to get 4950 )