Let $$S_1 = \sum_{j=1}^{10} j(j-1)\,^{10}C_j$$, $$S_2 = \sum_{j=1}^{10} j\,^{10}C_j$$ and $$S_3 = \sum_{j=1}^{10} j^2\,^{10}C_j$$. Statement-1: $$S_3 = 55 \times 2^9$$. Statement-2: $$S_1 = 90 \times 2^8$$ and $$S_2 = 10 \times 2^8$$.

A

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is false

C

Statement-1 is false, Statement-2 is true

D

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1