  In this paper, we find an explicit formulas, or recurrences, in terms of
generating functions for the cardinalities of the sets $S_n(T;\tau)$ of all
permutations in $S_n$ that contain $\tau\in S_k$ exactly once and avoid a
subset $T\subseteq S_3$, $|T|\geq2$. The main body of the paper is divided into
three sections corresponding to the cases $|T|=2,3$ and $|T|\geq4$.
