For $$r = 0, 1, ...., 10$$, let $$A_r, B_r$$ and $$C_r$$ denote, respectively, the coefficient of $$x^r$$ in the expansions of $$(1 + x)^{10}, (1 + x)^{20}$$ and $$(1 + x)^{30}$$. Then
$$\sum_{r=1}^{10}A_r(B_{10}B_r = C_{10}A_r)$$ is equal to

A

$$B_{10} - C_{10}$$

B

$$A_{10}\left(B_{10}^{2} - C_{10}A_{10}\right)$$

C

0

D

$$C_{10} - B_{10}$$