Question

2 corrected exams are being returned to each of n students. How many ways can the teacher give those 2 exams back to each student such that everyone receives at least 1 exam that is not his.

Answer 1

@satellite73 @jim_thompson5910 @dumbcow @dan815

Answer 2

@Zarkon @wio @perl

Answer 3

@zepdrix

Answer 4

lol @kropot72

Answer 5

For each set of 2 corrected exams for a particular student there are 2 combinations where only one returned exam is his and the other returned exam is not his. Therefore there are 2^n ways of returning the exams where exactly one of each student's exams is not his.
There are n! possible permutations of the n correctly returned exams for each of the 2^n ways of returning exactly one exam that is not his to each student. In many of these permutations students will receive 2 exams that are not theirs.
Therefore the number of ways that the teacher can give those 2 exams back to each student such that everyone receives at least 1 exam that is not his is given by:
\[\large 2^{n} \times n!\]