How many colors will be there in color cartridge?

It depends on the file's color mode (RGB or CMYK), and the output printer.

Most Computer Monitors are RGB (Red, Green, and Blue) color based, as are the majority of printers used by most non-professional users. As such, the file you're working in should be RGB, and rendered/printed as RGB to ensure what you see on screen will look like what's printed on paper.

Print publishing graphics have always used a 4 color process, CMYK (Cyan, Magenta, Yellow and Black). In addition to the file being CMYK, the output printer should also be CMYK. Many higher-end printers are now CMYK.

Sharp's new Aquos Quattron monitor technology is a step toward finally making monitors 4 colors instead of the CRT based 3 colors they were originally designed to handle.