It is typically taught that there are seven colors in the rainbow and can be remembered by the mnemonic device Roy G Biv: Red, Orange, Yellow, Green, Blue, Indigo and Violet.
An easier way of remembering the seven colours of the rainbow is by this expression: "Richard Of York Gave Battle In Vein." However, indigo and violet are close enough on the color wheel to represent the secondary color resulting from the combination of primary colours red and blue. An alternate answer is 6 for cases in which either indigo or violet is omitted or both are replaced with the term "purple".
If you are referring to how many colors in terms of big numbers, it's pretty much infinity, but a smaller infinity than how many colors there are. For example, black, white, brown, and pink are not in the rainbow.
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