# If there are 12 persons in a party and if each two of them shake hands with each other, how many handshakes are possible?

With 12 people , we need to choose a subset of two different people where order does not matter. Also, we need to choose all such subsets because each person is shaking hands with everyone else exactly once. The number of ways is: nCr

Where:n=12 & r=2

nCr= 12C2

12C2=

15C11=

15C11=

15C11=

15C11=66

Ans:In total 66 handshakes are possible,if there are 12 persons in a party and if each two of them shake hands with each other

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Challenging Quiz on P&C | Test Yourself55 mins
Lecture on Combinations49 mins
Interactive Quiz on Division and distribution of objects17 mins
Understand Permutations like never before60 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Interactive Quiz on Combinations50 mins
Combinations - BOX & GAP Method38 mins
Interactive Quiz on Combinations-0253 mins
Circular permutations61 mins
Division and distribution of objects58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses