Ericius

You are looking for the number of permutations when you pick three things from a group of thirteen.

So
${n! \over (n-m)!}$ where n=number of things in group and m=number of things you want to pick

$x = {13! \over (13-3)!}$

$x = {13! \over 10!}$
13*12*11

1716

Why does it work like that?

--->
Which one is going to be the bait?
One of these 13 people.
Which one is going to be the hook?
One of these 12 people that are not the bait already
Which one is going to be the bandit?
One of the 11 people left.
​So you have 13*12*11=1716 possible handshakes