There are 300 students currently enrolled in STAT 200. Among the 300 students, 150 students have taken MATH 106, and 120 students have taken MATH 012. We also know that 100 students have taken both courses. Find the probability that a randomly selected student takes neither MATH 012 nor MATH 106. (Show work and write the answer in simplest fraction form).
You need to come up with a 4-character password for your safe. The first two characters have to be two different letters of the alphabet, where each letter is used only once, and the last two characters have to be two numbers from 0 to 9, where the numbers are not necessarily different. How many different possible passwords are there? (Show work)