How many ways are there to arrange five different letters so that none of them are in their previous positon?
If we have five different letters $a$, $b$, $c$, $d$ and $e$, we have to find the number of all possible ways of permutations such that $a$ is not in the 1st position, $b$ is not in the 2nd position, $c$ is not in the 3rd position; $d$ is not in the 4th position and $e$ is not in the 5th position of the word. I have tried the question using a brute force approach and found the answer to be 44. How can I solve this problem using combinatorial rules and theorems?
