A 1080p monitor has:
1,920 × 1,080 = 2,073,600 pixels
Each pixel can display 32-bit color, which equates to:
2^32 = 4,294,967,296 colors
So, while each pixel can display one of 4.3 billion colors, the monitor can display combinations of those colors across its 2,073,600 pixels. The total number of possible color combinations on the screen is astronomical.
The actual number of possible combinations is:
4,294,967,296^2,073,600