[This problem is worth 4 points.]
The Star Tours ride at Disneyland is composed of four parts, and the content of each part is randomly determined. In the first part, the rider encounters either (a) Darth Vader or (b) Hans Solo and the Millennium Falcon. In the second part, the rider crash lands on either (a) Hoth, (b) Tatooine, or (c) Kashyyk. In the third part, the rider receives a video message from either (a) Admiral Ackbar, (b) Princess Leia, or (c) Yoda. In the fourth and final part, the rider is chased through either (a) Coruscant, (b) Naboo, or (c) an under-construction Death Star orbiting Geonosis.
Sophia wants to experience all of the eleven component pieces of the Star Tours ride. She doesn't care whether she experiences all 54 possible ride combinations, but wants all of the component pieces. Assuming that in each part, the encounter is randomly determined with equal probabilities, and that the selection of component piece is independent between parts, how many times does Sophia need to ride Star Tours to have at least a 90% chance of experiencing all eleven component pieces?
