Let `theta=(a_(1),a_(2),a_(3),...,a_(n))` be a given arrangement of `n` distinct objects `a_(1),a_(2),a_(3),…,a_(n)`. A derangement of `theta` is an arrangment of these `n` objects in which none of the objects occupies its original position. Let `D_(n)` be the number of derangements of the permutations `theta`.

The relation between `D_(n)` and `D_(n-1)` is given by

A. `D_(n)-nD_(n-1)=(-1)^(n)`

B. `D_(n)-(n-1)D_(n-1)=(-1)^(n-1)`

C. `D_(n)-nD_(n-1)=(-1)^(n-1)`

D. `D_(n)-D_(n-1)=(-1)^(n-1)`