Let the set [S=2,4,8,16, , 512] be partitioned into 3 sets A, B, C with equal number of el…

Question

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:

Accepted Answer

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 $C$)

$$={ }^9 C_3 \cdot{ }^6 C_3 \cdot{ }^3 C_3=1680$$

Solutions · 1