What are the two parts of a typical stamen?

The correct answer is Option (1) → Filament and anther

The stamen is the male reproductive organ of a flower. It has two parts: a long, slender stalk called the filament and a bilobed anther at its tip, where pollen grains are made. The lower end of the filament is attached to the thalamus or the petal of the flower, but these are other parts of the flower, not parts of the stamen.

Epidermis, endothecium, middle layers and tapetum are the four wall layers of the anther (the microsporangium). They are parts inside the anther, not the two parts of the stamen.

NCERT Extract:
Stamen, Microsporangium and Pollen Grain – “Figure 1.2a shows the two parts of a typical stamen – the long and slender stalk called the filament, and the terminal generally bilobed structure called the anther. The proximal end of the filament is attached to the thalamus or the petal of the flower. The number and length of stamens are variable in flowers of different species.”

Figure 1.2 (a) A typical stamen; (b) three–dimensional cut section of an anther