6.19 A professor assigns five problems to be completed as homework. At the next class meeting, two of the five problems will be selected at random and collected for grading. You only completed the first three problems.

a. What is the probability that you will be able to turn in both of the problems selected? (Hint: You can think of the problems as being labeled A, B, C, D, and E. Then one possible selection of two problems is A and B. If these are the two problems selected and you did problems A, B, and C, you will be able to turn in both problems. There are nine other possible selections to consider.)

b. Does the probability that you will be able to turn in both problems change if you had completed the last three problems instead of the first three problems? Explain.

c. What happens to the probability that you will be able to turn in both problems selected if you had completed four of the problems rather than just three?