Question 38562
This can be done a couple of ways...
Let me explain it this way.
The first of 8 people can shake hands with 7 people.
The second of 8 people can shake hands with 6 people (he has already shaken hands with the first).
And it goes on like this, so that the number of total handshakes for the 8 people is
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 handshakes
leaving 4 handshakes by the ninth person, which makes the total of 32.