"5 choose 2":
Canxcel the two 2's into the 4
Cancel the 3's
You are left with
or
ahndshakings.
If the people are A,B,C,D, and E, they are
1. A shakes hands with B
2. A shakes hands with C
3. A shakes hands with D
4. A shakes hands with E
5. B shakes hands with C
6. B shakes hands with D
7. B shakes hands with E
8. C shakes hands with D
9. C shakes hands with E
10. D shakes hands with E
Edwin