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 $$\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$$

Accepted Answer

Given set $S={{2}^{1},{2}^{2},\ldots {2}^{9}}$ 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