$$1 cm^{3}$$ of pure Germanium at $$20^\circ$$C contains about $$4.2 \times 10^{22}$$ atoms, $$2.5 \times 10^{13}$$ free electrons and $$2.5 \times 10^{13}$$ holes. 0.001% of Arsenic doping donatesan extra $$10^{17}$$ free electrons in the same volume. The approximate humberof holes in one $$cm^{3}$$ in the doped semiconductor under equilibrium condition is :

A

$$6.25 \times 10^{9}$$

B

$$2.5 \times 10^{9}$$

C

$$10.5 \times 10^{9}$$

D

$$10^{17}$$