If there are 76 persons in a party and if they shake hands with each other, how many handshakes are possible

Question

Question

Answer 1

Concept:

The number of ways to select r things out of n things is given by ⁿC_r

\(\rm ^nC_r=\frac{n!}{(n-r)!×(r)!}=\frac{n×(n-1)×....(n-r+1)}{r!}\)

Calculation:

We have to select 2 persons out of 76 for handshakes.

\(\therefore \) Number of handshakes = \(\rm ^{76}C_2=\frac{76×75}{2× 1}\)

= 38 × 75

= 2850

Hence, option (3) is correct.