The Kirkwood-Buff (KB) theory of solution is applied to a ternary mixture by deriving explicit expressions for the various Kirkwood-Buff integrals (KBIs) and the corresponding excesses of the number of molecules around central ones. However, the ideal solution should be considered non-aggregated, and the above expressions for the excesses provide non-zero values for such a case. For this reason, in order to obtain information about clustering one must subtract from the traditional excesses those which correspond to a reference state, thus ensuring that for an ideal mixture the excesses are zero. The expressions derived for the latter excesses have been applied to the investigation of the N,N-dimethylformamide-methanol-water mixture, to conclude that: (i) in the vicinity of the water molecules there are excesses of water and N,N-dimethylformamide molecules and a deficit of methanol molecules; (ii) in the vicinity of the methanol molecules there are excesses of methanol and N,N-dimethylformamide molecules and a deficit of water molecules; (iii) in the vicinity of the N,N-dimethylformamide molecules there are excesses of methanol and water molecules and a deficit of N,N-dimethylformamide molecules: (iiii) the excesses of N,N-dimethylformamide around water and methanol molecules and those around N,N-dimethylformamide are weakly dependent on the concentration of the third component in a large range of concentrations of the latter, and these results are compatible with the existence of N,N-dimethylformamide-water and N,N-dimethylformamide-alcohol complexes.