I painted a quick study of my wife putting on her makeup. The whole painting was done using only the primary colors with raw umber and white. The three primaries that I used are cadmium red light, cadmium yellow light and ultramarine blue.
Using a limited palette forces you to mix your own colors instead of having one pre-made; and in doing so you have a track as to how you came up to a particular color. Some old masters went as far as to only use primaries in all their work. One of them was Anders Zorn who used only ivory black, yellow ochre, cadmium red light and white. In theory you should be able to mix all other colors from just those three primaries with black and white.