JEE MAIN - Mathematics (2024 - 5th April Evening Shift - No. 13)
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:
1640
1520
1710
1680
Explanation
Given set $$S=\left\{2^1, 2^2, \ldots 2^9\right\}$$ which consist of 9 elements.
Maximum number of possible partitions (in set $$A, B$$ and $$C$$)
$$={ }^9 C_3 \cdot{ }^6 C_3 \cdot{ }^3 C_3=1680$$
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