Question 983010
If 8 people meet each other at a meeting by shaking hands with one another how many handshakes take place?

the answer I think is (8*7)/2 = 28 handshakes, but I don't understand it. Why is it 8*7 I know there are 8 people but why the 7? it's confusing me. Wouldn't it be a lot more. Maybe I just don't understand multiplication or something. Please explain what I don't understand about this.

Thank you
<pre>One way to look at this is that a person doesn't shake hands with him/herself. Each handshake requires 2 people so how many groups
of 2 people can be formed from a group of 8 people, taking 2 at a time? We use combination, with n = 8, and r = 2, for the following:
{{{" " [n]C[r]}}} = {{{" "[8]C[2]}}} = {{{8!/(6!*2!)}}} = {{{(8 * 7 * 6!)/(6!*2!)}}} = {{{(8 * 7 * cross(6!))/(cross(6!)*2!)}}} = {{{56/2}}} = {{{highlight_green(28)}}} 
It's as simple as that!!