1. Suppose we select a random sample of 3 numbers between 1 and 50, sampling without replacement.

a.How many samples of size 3 are possible? (2 marks)

b. What is the probability that the sum of the values in our sample is less than 9? (3 marks)

2. An intro Stats class has a total of 70 students: 15 Psychology majors, 10 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? (2 marks)

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. (2 marks)

c. What is the probability that a random sample of 6 students from this class has no two students with the same major? (2 marks)