If there are 20 persons in a party and if each two of them shake hands with each other,
how many hand shakes happen in the party ?
will it be 20C2 = 20*19 or 19+18+…+1? there are 2 different explanation and both seem to be logically correct
i said it 20C2 because suppose there re 4 people. A B C D. so the possible hand shakes are
{(AB), (AC), (AD), (BC), (BD), (CD)} =6 = 4c2
another way is 19+18+..+1. can somebody explain? answer is 380 or 190?
Best Answer
First of all there is no Probability here, perhaps Combinatorics/Graph theory is more appropriate.
$6$ is also $\binom{4}{2}$ but more importantly it is $3+2+1$.
Thus in all cases the number of hand shakes is $(n-1)+(n-2)+ \cdots + 1 = n(n-1)/2$. Count person by person, ignoring handshakes with people already counted, to see this.
190 is the answer.