Triple Product Can Hold Without Pairwise Independence

Let $\Omega = \{1,2,\ldots,8\}$ with uniform probability. Define events: $$A = \{1,2,3,4\}, \quad B = \{1,2,3,5\}, \quad C = \{1,4,6,7\}.$$ (a) Show that $P(A \cap B \cap C) = P(A)P(B)P(C)$. (b) Check whether each pair $(A,B)$, $(A,C)$, $(B,C)$ is independent. (c) What does this reveal about the relationship between the triple-product condition and pairwise independence?