An intro Stats class has total of 60 students: 10 Psychology majors, 5 Sociology majors, 5 Math majors, 6 Comp Sci majors, 4 Econ majors, and 30 undeclared majors. The instructor wishes to obtain a random sample of 6 students from this class.
a) How many different samples are possible?
b) How many different samples of size 6 are possible subject to the constraint that no 2 students may share the same major? For the purpose of this question, assume undeclared is a type of major.
c) What is the probability that a random sample of 6 students from this class has no two students with the same major?
d) Randomly choose 6 students from this class, what is the probability that at least two of them have the same major?
