Let $n ≥7$, and let $C$ be a collection of 15 distinct 5-element subsets of [n]. Prove that it is possible to color each element of $[n]$ yellow or orange so that each set belonging to $C$ has elements of both colors.
I know this is an applicaiton of Ramsey theory, but I'm not sure how to approach it since we could pick any n more than 7.
Maybe I'm completely wrong and it might not be ramsey theory related!
Also, I'm not sure how we'd relate this to a graph since we're coloring elements (vertices) as opposed to the edges themselves.