In Finn's preschool, each student is assigned a unique color palette of 3 colors for a finger-painting project. Different students may have 1 or 2 colors in common, but no 2 students have the same 3 colors. It there are 10 students in the class, how many different colors are required?
4 5 6 7 8

I have the correct answer of 5, but I basically made a list of color swatches to get the answer. Is there a faster way (save test time)?

Thank you