sandy wrote:
A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each person shakes hands exactly once with each of the other people in the room?
(A) 12
(B) 22
(C) 66
(D) 132
(E) 244
Here's an approach that doesn't require any counting techniques:
person shakes hands exactly once with each of the other people in the roomSo, each person shakes hands with 11 people.
So, we have 12 people, and each experiences 11 handshakes, for a total of
132 handshakes.
IMPORTANT: at this point, we need to recognize that every handshake has been counted
TWICE.
For example, if Person A and Person B shake hands, then Person A counts it as a handshake, AND Person B also counts it as a handshake.
Of course only one handshake occurred.
To account for the DUPLICATION, we'll divide
132 by
2 to get 66 handshakes
Answer: C
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep