Step 1:
Nāstika systems do not accept Vedic authority.
Step 2:
Bauddha, Jaina, Cārvāka, and Sautrāntika traditions are considered Nāstika.
Step 3:
Classical Sāmkhya accepts Vedic authority and is regarded as Āstika.
Step 4:
Therefore, the correct set is:
\[
B,\; C,\; D,\; E
\]
Hence, the correct answer is:
\[
\boxed{\text{(3) B, C, D, E Only}}
\]