To solve this problem, we need to determine the color code for a carbon resistor with a resistance of $(47 \pm 4.7)$k$\Omega. \\$The color code for resistors is based on the following scheme:$\\$• The first two bands represent the first two significant digits of the resistance value.$\\$• The third band represents the multiplier (the power of ten).$\\$• The fourth band represents the tolerance.$\\$Let's break down the given resistance value:$\\$• The resistance is $47$k$\Omega,$ which is $47000$ $\Omega. \\$• The first two significant digits are $4$ and $7. \\$• The multiplier is $1000$ (or $10^3$).$\\$• The tolerance is $\pm 4.7$k$\Omega,$ which is $\pm 10\%$ (since $4.7$ is $10\%$ of $47$).$\\$Using the resistor color code chart:$\\$• The color for the digit $4$ is Yellow.$\\$• The color for the digit $7$ is Violet.$\\$• The color for the multiplier $10^3$ is Orange.$\\$• The color for the tolerance $\pm 10\%$ is Silver.$\\$Therefore, the color code sequence for the resistor is:$\\$Yellow – Violet – Orange – Silver.$\\$This corresponds to Option 2.