Mathematics - Sets and Relations Question with Solution | TestHub

Let the set $S=\{2,4,8,16,\dots ,512\}$ 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 $\mathrm{A}\cap \mathrm{B}=\mathrm{B}\cap \mathrm{C}=\mathrm{A}\cap \mathrm{C}=\varphi$. The maximum number of such possible partitions of $S$ is equal to: