At a business meeting, every person shakes hand with each others once. If there were 91 handshakes in total, the number of people at the meeting is

Question

At a business meeting, every person shakes hand with each others once. If there were 91 handshakes in total, the number of people at the meeting is (A) 14 (B) 15 (C) 24 (D) 46

Tardigrade Admin · Accepted Answer

n C2=91 ⇒ (n(n-1)/2)=91 ⇒ n=14

Q. At a business meeting, every person shakes hand with each others once. If there were 91 handshakes in total, the number of people at the meeting is

14

15

24

46

$^{n} C_{2} = 91 \Rightarrow \frac{n ( n - 1 )}{2} = 91 \Rightarrow n = 14$

Q. At a business meeting, every person shakes hand with each others once. If there were 91 handshakes in total, the number of people at the meeting is

14

15

24

46

nC2​=91⇒2n(n−1)​=91⇒n=14

$^{n} C_{2} = 91 \Rightarrow \frac{n ( n - 1 )}{2} = 91 \Rightarrow n = 14$