In a plant,three dominant genes $A$,$B$,and $C$ must be expressed together to produce purple flowers. If any one or all three genes are in the recessive state,the flowers become colorless.
Raw material $\xrightarrow{A} X \xrightarrow{B} Y \xrightarrow{C} Z$ (Pigment)
$A$ purple-flowered plant with genotype $AABBCC$ is crossed with a colorless plant with genotype $aabbcc$. This results in $F_1$ hybrid purple offspring. What will be the proportion of purple-flowered plants in the $F_2$ generation produced by selfing the $F_1$ generation?

• A
  $\frac{27}{64}$
• B
  $\frac{1}{64}$
• C
  $\frac{9}{64}$
• D
  $\frac{37}{64}$