Conductivities of water and a saturated solution of a sparingly soluble salt $\mathrm{AB_2}$ are $7$ and $21\,\mu\mathrm{S\,m^{-1}}$, respectively. Given, $\lambda^{o}_{A^{2+}}=12.72\,\mathrm{mS\,m^{2}\,mol^{-1}}$ and $\lambda^{o}_{B^{2-}}=7.64\,\mathrm{mS\,m^{2}\,mol^{-1}}$, the solubility of $\mathrm{AB_2}$, in $\mathrm{mol\,m^{-3}}$, is
(a)$5.0 \times 10^{-4}$
(b)$5.0 \times 10^{-3}$
(c)$5.0 \times 10^{-5}$
(d)$5.0 \times 10^{-6}$