32-bit color has two parts to it:
color is support by the first 24 bits
translucency per shade of color is supported by the last 8 bits
So do 2^24 in your calculator and you'll get your answer. I don't have a calculator with me right now. But It's supposted to be like 16.7million colors.
Oh wait. another way of doing it is. 8 bits for each primary color: red, blue, green. 8 bits = 256 combinations per color. So multiply 256 x 256 x256 and it will give you 16.7million colors. If you want to factor in the transulcency multiply in another 256.