Four if you're getting a specific model in the US and one if you're looking for the other models or if you're not from the US.
Those four are Cobalt blue, Burgundy red, Graphite gold and Platinum and they are available on the Core i5 8gb model if I am not mistaken. Platinum is the color that is "default color" for all Surface products so all other configurations and other regions are getting just that color option.