1. A color estimation system comprising: a correlation memory unit that stores a correlation model that accepts an input of an image or information of the image, and outputs an ink-color set that is a color combination of inks used in reproducing the image by printing; and a color combination extracting unit that extracts the ink-color set corresponding to a print image, which is an image to be printed, by providing an input of the print image or image information of the print image to the correlation model, wherein the correlation model is generated by performing machine learning that establishes correlation between the image information and the ink-color set such that the ink-color set is outputted based on the image information, using a reference image of which the ink-color set necessary for printing is known in advance.