A professor does not like to grade, and he randomly assigns each student a letter grade of A, B, C, D, or F. In other words, a student has an equal chance of receiving each one of the five letter grades. Assume that each student's grade is independent of another student's grades. There are four students in the class. What is the probability that
a. All four students get an A?
b. All four students get a C or better?
c. None of the four students get an A?
d. At least one student gets an F?
Now assume that the professor does not want to fail more than one student. If one student fails, each succeeding student will receive a letter grade of A, B, C, or D with equal probability.
e. In a class of four students, what is the probability that the first student gets an F and the next three students all get an A?