CMYK question...

Hi

If an 8 bit image in RGB has 256 levels of colour in each channel
R 256
G 256
B 256
and to get the number of colours in an RGB image you multiply 256x256x256 which gives 16 million colours -

Why does a CMYK image have less colours available in its gamut when there are four channels rather than three, like this:
C 256
M 256
Y 256
K 256 Multiplied together giving 4.2 Billion colours

What's wrong with my thinking?

Any help, very much appreciated. Thanks.

CMYK is ink

Blimey!

When you convert and RGB image to a CMYK image it is still a set of pixels, but with tonal adjustments for ink printing (why am I having to explain this?).

But until you print the pixels are pixels and I am enquiring as to whether the colour range of CMYK is less than RGB whilst on the screen.

Perhaps I should have made this clearer in the original post.