The number of derangements of n objects, denoted by d(n), satisfies the recurrence relation : d(n)=nd(n-1)+1 or nd(n-1)-1, depending on whether n is even or odd. We have proved in a previous paper how a combinatorial model different from the usual derangement model provided a simple proof of the forementioned recurrence. This model has been further exploited and embedded in the context of symmetric functions. It is also possible to obtain explicit formulas for the q-derangements and also to study the reduction of the mahonian statistics modulo n. In this paper we show how the notion of reduced major index yields a direct interpretation of the above formula.