number of handshakes

aditya.j wrote:12 People meet in a party and each person shakes hand with every one else. What is the minimum number of handshakes ?
a)6
b)66
c)132
d)11!
e)12!

Another approach (other than 12C2) is this:

If we ask each person, "How many people did you shake hands with?" we'll find that each person shook hands with 11 people, which gives us a total of 132 handshakes (since 12x11=132).

From here we need to recognize that each 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 counts it as a handshake.

So, to account for the duplication, we'll divide 132 by 2 to get 66 (B)

Cheers,
Brent

ankush123251 wrote:@Brent-Isn't that the exactly reason why we have not done 12P2 and 12C2 because the order does not matter!!

Exactly.

Cheers,
Brent