Spermatogonia undergo a series of cell divisions to produce sperms. Select the correct statements from the following:
$A$. Spermatogonia always undergo meiotic cell division.
$B$. Primary spermatocytes divide mitotically to produce secondary spermatocytes.
$C$. Secondary spermatocytes, through their second meiotic division, produce spermatids.
$D$. Spermatids produce spermatozoa through mitosis.
$E$. Spermatids transform into spermatozoa by spermiogenesis.
Choose the correct answer from the options given below:

• A
  $(1)$ $A, C$ and $E$ only
• B
  $(2)$ $C$ and $E$ only
• C
  $(3)$ $A$ and $E$ only
• D
  $(4)$ $B, C$ and $D$ only