Partition_Equation_v2

Let group $G$ act on a finite set $X$. Let the distinct orbits of $X$ under the action of $G$ be $\Orb {x_1}, \Orb {x_2}, \ldots, \Orb {x_s}$ Then $\card X = \card {\Orb {x_1} } + \card {\Orb {x_2} } + \cdots + \card {\Orb {x_s} }$