A. Explain the reason why the cell requires a mechanism for identifying specific sequences of DNA. ...

A. Sequence information contains indicators important for the regulation of gene expression and DNA packaging. Examples include sequence indicators for where a gene starts and ends, where transcription begins, and where to assemble specific protein complexes at specialized sequences such as those found in telomeric or centromeric DNA.
B. Because 46 (= 4096) different sequences of six nucleotides can occur in DNA, any given sequence of six nucleotides would be expected to occur on average once in a DNA strand 4000 bases long, assuming a random distribution of sequences.
C. Short recognition sequences do not have as many sequence-specific contacts (which means they don't bind as tightly to the binding site in question), and they are more likely to be found randomly throughout the genome. Using the same type of calculation from part B, there are 256 possible combinations for a 4-base-pair recognition sequence, which could be found 1516 times over a 4000-base-pair segment by random chance. This could be useful for proteins that need to bind to a large number of sites with low affinity. If we take the case of the 8-base-pair sequence, there are 65,536 different possible sequences. So, not only do they represent high-affinity binding sites, they are much less likely to be found by random chance.