Hi Mike,
Yes it can be done with a little work and planning by using a description question type for each passage, but it will not be completely random because you cannot randomly select description question types to go in a quiz. You have to manually place them in a test, but then you can randomly select questions to go with the passage.
For each passage, create a separate question category...so you are going to need 20 of them. Any question you create for each passage, needs to be in the same category as the passage it applies to so that you can force the random selection process to get questions that match the passage. Now, when you create your quiz make it 3 pages, you pick three passages and put it's description as the first question on a page. Then randomly select actual questions from it's category. You decide however many questions you want to go with the passage that is in the description for the page. Repeat for your other pages.
Make other versions of the quiz by using other passages paired with the correct questions.
Personally, I think it would be easier to make 20 separate quizzes and decide at the last moment, which three you want have the students take.
Alternative 1 - if the passages are short just include them in the question, then you can randomize the whole quiz but your students might wind up having to answer questions from many passages instead of 3.
Alternative 2 - Use a CLOZE type question. Put your passage first, and then a bunch of questions right after it as part of the same CLOZE question. Can't randomly decide what questions, since they would all be part of the same CLOZE question, but you could make multiple versions.
