Well, grammatically possible but semantically , I mean meaning, it sounds strange. Everyone knows that a rainbow is colourful so you don't have to say this again.
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GoodmanThis rainbow has many colours.
Is there another black and white rainbow that we don't know about?http://www.EnglishForward.com/imgres?imgurl=http://www.entheosweb.com/images/photoshop/rainbow_6.jpg&imgrefurl=h