At the first meeting of a 12-member student council, every member shakes hands exactly once with every other member. How many handshakes take place?

Explanation

1. 01

   Each handshake is a pair of members, and the pair (A, B) is the same as (B, A).

2. 02

   Handshakes $= {}^{12}C_{2} = \frac{12 \times 11}{2} = 66$.