At a party, every two people shook hands once. How many people
attended the party if there were 66 handshakes? Options.
A) 12 B) 22 C) 33 D) 65 E) 67
If there are n people at the party, then each of the n people will shake hands   with n -1 other people. Since each handshake accounts for a handshake that each of two   people have made (i.e., since there are two people involved with each handshake), the total   number of handshakes the n people will make is n(n-1)=2. (Alternatively, the number   of handshakes is the number of ways of choosing 2 people from among n people, which is   -n   2 =n(n-1)=2.) Hence, we have n(n-1)=2 = 66 = 12 11=2, so n = 12.   correct answer 12
<result>A</result>
At a party, every two people shook hands once. How many people
attended the party if there were 66 handshakes?