Thread: Handshakes

there are 12 friends. each greeted each other by shaking hands. how many handshakes took place.

Use principle of counting

Originally Posted by BAdhi

Use counting principle

I could do it in that way but is there any other way because it will take a long time to get the answer that way....xD

why do you say it takes a long time to get the answer, if there are n objects and 2 slots for objects, no of permutations are equal to n(n-1). Since there changing two objects in a group(a,b and b,a) doesn't make a difference divide it by 2

Originally Posted by MoniMini

I could do it in that way but is there any other way because it will take a long time to get the answer that way....xD

What that tells me is that you do not know what the "principle of counting" is! No, it does not mean "write out all the possible handshakes and count them up".

There are 12 friends and each shakes hands with each of the 11 others. The "principle of counting" says there are 12*11 "handshakes". But that counts the handshake between "Andy" and "Barbara" twice- once for Andy and once for Barbara. So, as BAdhi says, divide by 2.