During the last class period of the semester, each student in a graduate computer science class with 10 students is required to give a brief report on his or her class project. The professor randomly selects the order in which the reports are to be given. Two students have been working on similar projects and would like to give their reports consecutively. What is the probability that this will happen?
Here's what I have (pretty sure this is wrong): C(10,2)/10! (10 choose 2 divided by 10 factorial)
There are $10!$ ways to order the students. If we consider the number of ways to order the other $8$ students and the pair of students, then there are $2\cdot9!$ ways to order them where the two students present consecutively. Therefore the probability is $$ \frac{2\cdot 9!}{10!}=\frac{2}{10}=\frac{1}{5} $$