Prove that the number of triples $\displaystyle (A, B, C)$ where $\displaystyle A, B, C$ are subsets of $\displaystyle {1, 2, ..., n}$ such that $\displaystyle A \cap B \cap C = \phi, A \cap B \ne \phi, B \cap C\ne \phi$ is $\displaystyle 7^n - 2.6^n + 5^n$.