1. A professor has written 6 different versions of an online test, for security reasons. Students are randomly assigned any one of the tests when they sign in to take it.
a) In how many ways can your 8 friends from the class be assigned the various versions of the test?
b) What is the probability that you and your 2 best friends will be assigned the same version?
2. Your company is going to build 4 factories that will use the latest robot technology. One will make prefab buildings, another sewer systems, a third will make prefab highway overpasses, and the fourth will build shipping containers The factories will each be in a different state, but all 50 states are eligible.
a) In how many ways can your factories be placed among the states?
b) If you have no idea which states will be chosen, what is the probability that all 4 factories will be located in the mid-Atlantic region?