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  4. The number of triplets (A, B, C) where A, B, C are subsets of X= 1,2,3, ldots ldots, 100 such that A ∩ B ∩ C=φ but A ∩ B ≠ φ and B ∩ C ≠ φ is

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Q. The number of triplets $(A, B, C)$ where $A, B, C$ are subsets of $X=\{1,2,3, \ldots \ldots, 100\}$ such that $A \cap B \cap C=\phi$ but $A \cap B \neq \phi$ and $B \cap C \neq \phi$ is

Permutations and Combinations

Solution:

For each elements there are 7 choices without any restriction $7^{100}$.

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