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?

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?