What is the number of permutations in which all number change position?
For example, suppose a ordered set (12345678...n)
What is the number of permutations this (below) is not allowed:
Let P be, let's say, the permutation operator, and a_{i} the element at the i position
Apply now P on the set, if $ai_{after, p} = ai_{before, p}$ for some i, so it is not allowed.
I am a little stuck because, i think we can not separate in little cases as, for example, "n! - (number o situations in which 1 remains 1)..." Since if we try that, we will need to consider the cases in which, let's say, 2 go for 1 or for another, and so on...
