The combination of red, green and blue hex values from 0-255 gives nearly 17,000,000 different colors. Shades of gray (white to black) are obtained by using equal hex values of red, green and blue. White is 255, 255, 255. Black is 0, 0, 0.
In the early days of the Web most people used monitors that could only display 256 colors. Statistics now show that the instance of 8-bit monitors has dropped to below 10% of the total Web users. Given that, it would be safe to assume that 90% of your target audience is using equipment that will display any one of the 1,700,000 colors you pick.