Subsets with Two Conditions

Problem

Let $S = \{1, 2, 3, \dots, 10\}$ . How many subsets $A$ of $S$ satisfy both

A \cap \{1, 2, 3\} \neq \varnothing \quad \text{and} \quad A \cup \{4, 5, 6\} \neq S?

Answer

Solution

Difficulty	4/10
Topics	combinatorics, Counting, Set Theory

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