Question

Let $A=\{1,2,3,4\}$. Find the number of different ordered pairs $(B,C)$ that can be formed such that $B\subset A,C\subset A$ and $B\cap C=\varphi$.

Answer 1

Answer: 0081

Each element of set A can be distributed in two sets $B$ and $C$ by 3 ways.
(The three ways are either only in B or only in C or in none of B and C).
So, the number of ways of distributing $=(3{)}^4\Rightarrow 81$ ways.