Question

A total of $28$ handshakes was exchanged at the conclusion of a party. Assuming that each participant was equally polite towards all the others, the number of people present was:

• A. $14$
• B. $28$
• C. $56$
• D. $8$
• E. $7$

Answer 1

Answer: (D)

$8$

Let n be the number of people present. Single out a particular individual P. P shakes hands with $(n-1)$ persons, and this is true for each of the n persons. Since each handshake is between two persons, the total number of handshakes is $n(n-1)/2=28.\therefore n=8;orC(n,2)=n(n-1)/2=28.$