In this talk we consider a concept which is the dual to the concept of a selectible space, namely, a $\mathrm{\Lambda }$-coselection space ($\mathrm{\Lambda }$ may be any given hyperspace of a space $X$). We consider this concept when $\mathrm{\Lambda }$ is the $n$th symmetric product $F_n(X)$. We present sufficient conditions for a continuum to be either an $F_2(X)$-coselection space or an $F_3(X)$-coselection space.