Algebraic S-integers of fixed degree and bounded height

Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S\uaf-integers of bounded height and fixed degree over k, where S\uaf is the set of places of k\uaf lying above the ones in S