The members of the Mathematics club shook hands once with each of the other members A total of 780 - Maths - Second Degree Equations

Question

The members of the Mathematics club shook hands once with each of
the other members A total of 780 shake hand took place Find how
many members are there in the club? 40 or – 39

Neha Sethi · Accepted Answer

Dear student
2)Let the total persons in the room be n
  As hand shake occurs between any two persons, so we need to select any two people out of n
  This can be done in nC2  ways  Given, total number of hand shakes =780nC2=780⇒n!2!(n-2)!=780⇒n(n-1)(n-2)!(n-2)!=1560⇒n(n-1)=1560⇒n2-n-1560=0⇒n2+39n-40n-1560=0⇒n(n+39)-40(n+39)=0⇒(n-40)(n+39)=0⇒n-40=0 or n+39=0⇒n=40 or n=-39As total number of persons cannot be negative
 So n≠-39So, n=40
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The members of the Mathematics club shook hands once with each of the other members. A total of 780 shake hand took place. Find how many members are there in the club? 40 or – 39