i think there will be 36 handshakes.
so the solution be like: (SORRY FOR MY SOLUTION)
the circles represent the handshakes of each person
so for person 1, the red circles represent the number of the handshakes he made.
and its also like in person 2, the orange circles represent the number of handshakes he made.
and so on..
so in total, there will be 36 handshakes.
ps i think we had this question when i was in grade 7, i just dont remember the answer.