Let the set $S=\{2,4,8,16, \ldots, 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$ and $$\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}=\mathrm{A} \cap \mathrm{C}=\phi$$. The maximum number of such possible partitions of $S$ is equal to:
Solution
<p>Given set $S=\left\{2^1, 2^2, \ldots 2^9\right\}$ which consist of 9 elements.</p>
<p>Maximum number of possible partitions (in set $A, B$ and $C$)</p>
<p>$={ }^9 C_3 \cdot{ }^6 C_3 \cdot{ }^3 C_3=1680$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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