Everybody in a room shakes hands with everybody else. The total number of handshakes is 66 . The number of persons in the room is

Question

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66 . The number of persons in the room is (A) 11 (B) 12 (C) 13 (D) 14

Tardigrade Admin · Accepted Answer

Let the number of persons in the room be n, then n C2=66 ⇒ (n(n-1)/2)=66 ⇒ n2-n-132=0 ⇒(n-12(n+11)=0 ⇒ n=12

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$ . The number of persons in the room is

11

12

13

14

Let the number of persons in the room be $n$ , then
$^{n} C_{2} = 66$
$\Rightarrow \frac{n ( n - 1 )}{2} = 66$
$\Rightarrow n^{2} - n - 132 = 0$
$\Rightarrow (n - 12 (n + 11) = 0$
$\Rightarrow n = 12$

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is 66 . The number of persons in the room is

11

12

13

14

Let the number of persons in the room be n, then nC2​=66 ⇒2n(n−1)​=66 ⇒n2−n−132=0 ⇒(n−12(n+11)=0 ⇒n=12

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$ . The number of persons in the room is

Let the number of persons in the room be $n$ , then
$^{n} C_{2} = 66$
$\Rightarrow \frac{n ( n - 1 )}{2} = 66$
$\Rightarrow n^{2} - n - 132 = 0$
$\Rightarrow (n - 12 (n + 11) = 0$
$\Rightarrow n = 12$