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

Question

( A ) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
( B ) Statement -1 is false, Statement-2 is true
( C ) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
( D ) Statement -1 is true, Statement-2 is false