Subject
Quantitative Aptitude
Topic
Permutation & Combination
At a party, everyone shook hands with everybody else. If there were 66 handshakes, how many people were at the party?
At a party, everyone shook hands with everybody else. If there were 66 handshakes, how many people were at the party?
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13Explanation
Let the number of persons= n Number of handshakes by first person= n- 1 (As he cannot handshake with himself) Number of handshakes by second person = n- 2 (As he has already handshaked with first person) Number of handshakes by third person= n- 3 . . Number of handshakes by second last i.e. ( n- 1)th person= n- (n- 1)= 1 Number of handshakes by last i.e. nth person= n- n= 0 So, Total number of handshakes=(n- 1)+ (n- 2)+ (n- 3)+ 1+ 0 = 0+ 1+ 2+ 3+ ...........(n- 1) = Sum of first (n- 1) terms = (n- 1)(n- 1+ 1)/2 = n(n- 1)/ 2 So, Total number of handshakes= n(n- 1)/2 According to question, n(n- 1)/ 2= 66 => n^2 - n= 132 => n^2- n- 132= 0 => n^2- 12n+ 11n- 132= 0 => n(n- 12) + 11(n- 12)= 0 => (n- 12)(n+ 11) = 0 n= 12 or n= - 11(which is not possible as no. Of persons cannot be negatRelated questions
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