Question

Add a meeting six people each one another by shaking hands. If each person must shake hands once with every other person in the room, how many handshakes occur in the meeting
A) 10
B) 12
C) 15
D) 16

Answer 1

The number of handshakes is the number of ways 6 objects can be selected 2 at a time.

.. C(6,2) = 6·5/(2·1) = 15

The appropriate choice is

... C) 15

_____

Consider that each person can shake hands with 5 others. That's a total of 6*5 = 30 handshakes, but it counts both A shaking with B and B shaking with A. If each pair of persons only shakes hands once, the number of handshakes is 30/2 = 15.