Handshake count among 12 people: If every pair of distinct persons among 12 shakes hands exactly once, how many handshakes occur?

Introduction / Context:
Each handshake corresponds to an unordered pair of people. Counting unique handshakes among n participants equals the number of 2-combinations C(n,2).

Given Data / Assumptions:

• n = 12 distinct people.
• One handshake per unordered pair.

Concept / Approach:

• Count unordered pairs: C(12,2).

Step-by-Step Solution:

Verification / Alternative check:
Degree-sum in complete graph K12: sum of degrees = 12*11; divide by 2 equals number of edges = 66 (handshakes).

Why Other Options Are Wrong:

• 55, 44, 77 are values of C(n,2) for other n or guesses.

Common Pitfalls:

• Double-counting ordered pairs; order does not matter for a handshake.

Final Answer:
66