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Herm and his 12 followers have created a not-so-secret ``handshake'' that involves three people. The first person (the hook) initiates the greeting by casting an invisible fishing line, and the second person (the bait) walks toward the first person as if the ``bait'' is being reeled via the invisible fishing line. When the bait is about to meet the hook, they both go up with hand as if to perform a ``high five.'' At that point, however, a third person (the bandit) steps in to ``steal'' the ``high five'' from the hook.

Within Herm's group, how many different handshakes are possible?

 Jan 21, 2019

\(here are $13$ people in Herm's group. The only purpose of the detailed explanation of the ``handshake'' is to illustrate that this is not a normal handshake, and that there is a distinct role for each of the three people involved in the handshake. There are $13$ possibilities for the hook, $12$ possibilities for the bait, and $11$ possibilities for the bandit. Therefore, we have $13 \cdot 12 \cdot 11 = \boxed{1716}$ total possibilites.\)

 Jul 20, 2019

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