If $x = (a-1)(b-2)(c-3)(d-4)(e-5)$, where $a,b,c,d,e \in \mathbb{N}$ are distinct natural numbers less than 6. If x is a non zero integer, then the how to count the no of sets of possible values of $(a,b,c,d,e)$?
which is the fastest (pencil-paper) solution of this problem?
$ \mathbb{N} = 1,2,3,\cdots $