1. 24 possible handshakes
2. 27 possible handshakes
3. 54 possible handshakes
For every 3 people there are 3 possible handshakes. If you add one more person making 4, there will be 6 possible handshakes. Every time you add a person you can add 3 to the number of handshakes you had before 3p (people) = 3h (handshakes). So 4p=6h 7p=15h and so on.
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