IT-CESENATICO 2011 Problem 6

Let $X = \{1, 2, 3, 4, 5, 6, 7, 8\}$ . We want to color, using $k$ colors, all subsets of $3$ elements of $X$ in such a way that, two disjoint subsets have distinct colors. Prove that: (a) $4$ colors are sufficient; (b) $3$ colors are not sufficient.