Solution
The Handshake Count
Show the problem again
At a party of 20 people, everyone shakes hands with everyone else exactly once. How many handshakes occur?
Worked solution
The answer is 190. Each handshake corresponds to an unordered pair of people, so the count is C(20, 2) = 20 · 19 / 2 = 190. Equivalently, each of 20 people shakes 19 hands, and dividing 20 · 19 by 2 corrects for counting each handshake twice.
Source: Standard application of the handshaking lemma from introductory graph theory. Statement written for AxiomIQ.