How many color variations can a 32-bit color palette display?

A 32-bit color palette can display 16,777,216 color variations. This is determined by the fact that 32 bits of color depth typically comprises 8 bits for each of the RGB (Red, Green, and Blue) channels, and an additional 8 bits which are often used for an alpha channel, providing transparency.

Each color channel (Red, Green, Blue) having 8 bits can produce 2^8 or 256 different values (from 0 to 255). When you combine the three channels together, the total number of colors can be calculated as:

256 (Red) x 256 (Green) x 256 (Blue) = 16,777,216 colors.

This allows for a wide range of colors, making 32-bit color depth suitable for applications requiring high fidelity in color representation, such as graphic design and gaming.

The higher options in the given choices, such as 1 billion, exceed the capabilities of the 32-bit representation, and the lower options like 256 and 32,768 refer to the limits of 8-bit and smaller color depths.