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Measurements of the associated production of a W boson and a charm (c) quark in proton-proton collisions at a center-of-mass energy of 8 TeV are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7 fb$^{-1}$ collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction $\sigma$(pp $\to$ W + c + $\sigma$(pp $\to$ W$^+$ + c + transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed.