Determine the number of unique sequences of length 15, consisting of x's and y's, and which contain either 10 consecutive x's or 5 consecutive y's. (`xyyyxyyyyyyyyyy' is an example of a sequence which should be counted).
I'm currently stuck on this question and have been getting some very large answers (e.g 46078) that I don't believe can exist.
Any assistance with the following question would be great: