A tablet screen; when "large icons" is selected in the display settings is divided into 3 rows and 4 columns into identical compartments, and when "small icons" is selected, it is divided into 5 rows and 6 columns into identical compartments as shown in Figure 2. In both cases, at most one application icon is placed in each compartment. When "large icons" is selected in the display settings, it is observed that the icons of all applications on the tablet are located in $\frac{2}{3}$ of the compartments on the screen. If the display settings are changed to "small icons", in what fraction of the compartments on the screen will the icons of all applications on the tablet be located? A) $\frac{1}{5}$ B) $\frac{1}{6}$ C) $\frac{3}{10}$ D) $\frac{4}{15}$ E) $\frac{7}{30}$
A tablet screen; when "large icons" is selected in the display settings is divided into 3 rows and 4 columns into identical compartments, and when "small icons" is selected, it is divided into 5 rows and 6 columns into identical compartments as shown in Figure 2. In both cases, at most one application icon is placed in each compartment.
When "large icons" is selected in the display settings, it is observed that the icons of all applications on the tablet are located in $\frac{2}{3}$ of the compartments on the screen.
If the display settings are changed to "small icons", in what fraction of the compartments on the screen will the icons of all applications on the tablet be located?
A) $\frac{1}{5}$
B) $\frac{1}{6}$
C) $\frac{3}{10}$
D) $\frac{4}{15}$
E) $\frac{7}{30}$