1. **State the problem:** We need to multiply a 1x3 matrix $A = [65\ 80\ 30]$ by a 3x2 matrix $B = \begin{bmatrix}1 & 10 \\ 2 & 15 \\ 8 & 55\end{bmatrix}$.\n\n2. **Recall matrix multiplication:** The product $C = A \times B$ will be a 1x2 matrix, where each element $c_{ij}$ is calculated as the sum of element-wise products of the $i$th row of $A$ and the $j$th column of $B$.\n\n3. **Calculate first element $c_{11}$:** Multiply corresponding elements of $A$ and first column of $B$ and sum:\n$$c_{11} = 65 \times 1 + 80 \times 2 + 30 \times 8 = 65 + 160 + 240 = 465.$$\n\n4. **Calculate second element $c_{12}$:** Multiply corresponding elements of $A$ and second column of $B$ and sum:\n$$c_{12} = 65 \times 10 + 80 \times 15 + 30 \times 55 = 650 + 1200 + 1650 = 3500.$$\n\n5. **Write the resulting matrix:**\n$$C = \begin{bmatrix}465 & 3500\end{bmatrix}.$$\n\n6. **Check the answer against options:** Option (a) proposes $[465\ 500]$ which is incorrect because second element is 3500, not 500.\nOption (b) proposes $[3500\ 465]$ which reverses the order and so is not correct either.\n\n**Final answer:** The correct product is $$\boxed{[465\ 3500]}.$$