Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

Question

Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is (A) 9 (B) 10 (C) 5 (D) 15

Tardigrade Admin · Accepted Answer

Number of handshakes = 45 ⇒ nC2 = 45 ⇒ n(n-1) = 90 ⇒ n = 10

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

9

10

5

15

Number of handshakes = 45
$\Rightarrow^{n} C_{2} = 45$
$\Rightarrow n (n - 1) = 90$
$\Rightarrow n = 10$

Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

9

10

5

15

Number of handshakes = 45 ⇒nC2​=45 ⇒n(n−1)=90 ⇒n=10

Number of handshakes = 45
$\Rightarrow^{n} C_{2} = 45$
$\Rightarrow n (n - 1) = 90$
$\Rightarrow n = 10$