Recycling questions from a question bank.

The obvious problem with non-simultaneous exams is that the first takers of the exam will alert subsequent takers to the test's content. To diminish the effectiveness of such commuication and of shoulder surfing, one can produce multiple distinct tests via a randomized selection of questions from a large question bank. Of course, organized groups, e.g., fraternities, can make a books of those questions by having their members and friends record and/or remember what was on an exam.^4.6

Maximizing the size of the question ban and minimizing the number of distinct exams that are issued hinders the rate and which such question coverage can be accomplished.^4.7 If we make random selections of questions from a bank of $n$ questions and put them in a book, the chances that the $(k+1)$-th selection is not already in the book is $((n-1)/n)^k$. Say that the bank has 500 questions and each exam has 25 of those questions randomly selected. If fourteen students who took distinct exams report the questions on their exams, the book will contain more than half of the questions in the bank, i.e., $(499/500)^{(25*14)}$ is less than a half.^4.8