We have 4 nucleotides (nitrogenous base). They are adenine(A), guanine(G), cytosine (C), thymine(T). According to question we have to synthesize a library containing all possible random hexamers. Hexamers contain 6 nucleotides means NNNNNN (N = any nucleotide it can be A or G or T or C). In hexamer, 4 nucleotides have 6 places to sit in any combination. In 6 places, 4 nucleotides can be arranged in 4^6 = 4096 ways. It means 4096 unique hexamers can be formed with as much as possible combinations . In 4096 hexamers, orientation of each nucleotides are different from one another therefore all are unique oligonucleotide sequence formed.
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