  For given simple graphs $G_1, G_2, \ldots , G_t$, the Ramsey number $R(G_1,
G_2, \ldots, G_t)$ is the smallest positive integer $n$ such that if the edges
of the complete graph $K_n$ are partitioned into $t$ disjoint color classes
giving $t$ graphs $H_1,H_2,\ldots,H_t$, then at least one $H_i$ has a subgraph
isomorphic to $G_i$. In this paper, for positive integers $t_1,t_2,\ldots, t_s$
and $n_1,n_2,\ldots, n_c$ the Ramsey number $R(S_{t_1}, S_{t_2},\ldots
,S_{t_s}, n_1K_2,n_2K_2,\ldots,n_cK_2)$ is computed, where $nK_2$ denotes a
matching (stripe) of size $n$, i.e., $n$ pairwise disjoint edges and $S_{n}$ is
a star with $n$ edges. This result generalizes and strengthens significantly a
well-known result of Cockayne and Lorimer and also a known result of
Gy\'{a}rf\'{a}s and S\'{a}rk\"{o}zy.
