The expected frequency of restriction site 5'GGCC-3' is once every 256 nucleotides. This is because the recognition sequence of the given restriction site is 5'-GGCC-3' in genome lets assume that the nitrogen bases are independent in recognition sequence.
Total types of nucleotides in DNA is four which is thymine, cytosine, guanine, adenine.
Total frequency of any sequence of "n" nitrogen bases is 1/4n where n is for nitrogen bases or GGCC.
Therefore the frequency is 1/4×4 which is equal to 1/256 is equal to once every 256.