Question

at a party everyone shake hands with everybody else there are 66 hands how many people wear at the party options are 30 14 12 10 25

Answer 1

Let there be n persons.

First person shakes hand with everyone else=n-1 times(n-1person)

Second person shakes hand with everyone else=n-2 (not with first as it's already done)

Third person shakes hands with remaining person=n-3

so total handshakes in the party =

(n-1) +(n-2)+(n+3)*.....0

=>(n-1)*(n-1+1)/2=(n-1)*n/2=66

=>n^2-n=132

=>(n-12)(n+11)=0

So n=12 or n=-11

-11 can be the answer to the answer is 12

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