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A measurement of \(b\)-hadron pair production is presented, based on a data set corresponding to an integrated luminosity of 11.4 fb\(^{−1}\) of proton-proton collisions recorded at \(\sqrt{s}=8\) TeV with the ATLAS detector at the LHC. Events are selected in which a \(b\)-hadron is reconstructed in a decay channel containing \(J/ψ → μμ\), and a second \(b\)-hadron is reconstructed in a decay channel containing a muon. Results are presented in a fiducial volume defined by kinematic requirements on three muons based on those used in the analysis. The fiducial cross section is measured to be 17.7 ± 0.1(stat.) ± 2.0(syst.) nb. A number of normalised differential cross sections are also measured, and compared to predictions from the PHYTHIA8, HERWIG++, MADGRAPH5_AMC@NLO+PYTHIA8 and SHERPA event generators, providing new constraints on heavy flavour production.