Question

If in a party, everybody shakes hands with everybody, and 36 hands are shaken , then how many people are there

Answer 1

Given:

Total hands shaken= 36

Everybody shakes hands with everybody

To find:

Total number of people present

Solution:

Let the total number of people be N

So, each person shakes hands with all except himself, and for one handshake two persons are required

Going by the formula we have:

Total handshakes= N! /(2!(N-2)! or

N(N- 1)/2

So,  N(N-1)/2 = 36

Or,   N^2 - N = 72

Or, N^2-N-72 = 0

On solving the quadratic equation we get the value of N as 9 or -8( discarded as negative,i.e. no of persons can't be a negative value).

Therefore, there are 9 people in the party.

Answer 2

Answer:

so, we get answer as 9...