# In a class of 20 students,every student had a hand shake with every other student.The total no of hand shakes were

$\begin{array}{1 1}(A)\;180\\(B)\;190\\(C)\;200\\(D)\;210\end{array}$

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• $C(n,r)=\large\frac{n!}{r!(n-r)!}$
Since every pair of the students gives us a handshake
$\therefore$ Total number of handshakes =Total number of pairs of students
$\Rightarrow$Number of ways of choosing two students out of 20 students
$\Rightarrow 20C_2=\large\frac{20!}{2!18!}$
$\Rightarrow \large\frac{20\times 19\times 18!}{2\times 18!}$
$\Rightarrow 190$
Hence (B) is the correct answer.
answered May 19, 2014