Question 10787
Have you studied Permutations and Combinations?

IF there were only 2 people,then only 1 handshake wld have occured

If 3 ppl, then 3 hand shakes

If 4 people then 6

If n people  then its nC2 or n(n-1)/2 

So if 78 handshakes = n(n-1)/2 = 78

n(n-1) = 78x2
       = 39 x2 x2
       = 13x3x2x2
      = 13x12
So 12people were at the party