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For an $n$-vertex graph $G$, let $N(S_{2,1},G)$ be the number of injective labeled copies in which the two red edges of $S_{2,1}$ are mapped to edges of $G$ and its blue edge is mapped to a non-edge of $G$, that is, \\begin{align*}\n  N(S_{2,1},G)=\n  \\sum_{v\\in V(G)} d(v)(d(v)-1)(n-1-d(v)). \\end{align*} For every fixed red edge density $\\beta\\in[0,1]$, we determine both extremal $S_{2,1}$-densities. 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