Two countries meet with 12 delegates each. Every delegate of one country shakes hands with every delegate of the other country (no intra-country handshakes). How many handshakes occur?

Introduction / Context:
This is a complete bipartite handshake count K(12,12): each of the 12 from Country A shakes with each of the 12 from Country B.

Given Data / Assumptions:

• Country A: 12 delegates; Country B: 12 delegates.
• Only cross-country handshakes are counted.

Concept / Approach:
Each of the 12 delegates in A shakes with 12 in B, giving 12 * 12 handshakes.

Step-by-Step Solution:

Verification / Alternative check:
Graph-theoretic model: number of edges in K(12,12) is 12*12.

Why Other Options Are Wrong:
72 halves the count incorrectly; 288 doubles it by counting both directions as distinct handshakes.

Common Pitfalls:
Accidentally including intra-country pairs or double-counting the same handshake.

Final Answer:
144