Suppose you are a biologist, you sequence a (very short) gene whose DNA sequence has length 21, and you observe that every time the nucleotide...

Suppose you are a biologist, you sequence a (very short) gene whose DNA sequence has length 21, and you observe that every time the nucleotide (symbol) A appears, it is followed by the nucleotide C. An immediate question is to wonder if that is something we can expect from a random sequence or if this might be exceptional enough that the biological function of this observation is investigated. To answer this we need to find the number of strings of size 21 over the alphabet {A, C, G, T } in which an A is always followed by a C