1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A= 1,2,3,4 . Find the number of different ordered pairs (B, C) that can be formed such that B ⊂ A , C ⊂ A and B ∩ C =φ.

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Q. 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 $B \cap C =\phi$.

Permutations and Combinations

Solution:

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.