Question

in a party each participant shook hands with each other of remaining participants and the number of such shakings was recorded to be 66 then the number of participants must be​

Answer 1

ans :12 participants

Answer 2

$\huge\boxed{\texttt{\color{yellow}{\fcolorbox{blue}{pink} {Hyyyy mate!!!}}}}$

Lets say there are n persons

first person shakes hand with everyone else: n-1 times(n-1 persons)

second person shakes hand with everyone else(not with 1st as its already done): n-2 times

3rd person shakes hands with remaining persons: n-3

So total handshakes will be = (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;

= n = 12 OR n =-11

-11 is ruled out so the answer is 12 persons.

HOPE IT HELPS!!!!