Q. Eleven friends meet at a party. Each one shakes hand with each of the others once. The number of possible hand shakes is
a) 65
b) 22
c) 55
d) 56
Correct Answer: c) 55
Question from UPPSC Prelims CSAT 2025
Explanation:
A handshake involves an unordered pair of people. With 11 friends, the number of unique pairs is C(11,2) = 11*10/2 = 55.
Alternatively, if each person shakes hands with 10 others, the naive count 11*10 double-counts each handshake, so divide by 2 to get 55.
