In the permutations of n objects, how many objects in every permutation are not in their place on average?
For example in the permutation (2314), the objects 1,2 and 3 are not in their place. Therefore, three objects are not in their place.
I tried to solve this by calculating the number of permutations with 1, 2, 3, ... objects not in their place one by one but it ends up wrong. Any idea how to solve it?